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[
{
"content": "Statement: Compute $\\binom{23228}{23228}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute $\\binom{23228}{23228}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the expectation of -4.3 x^2-1.2 x-1.1 where $x \\sim $ \\text{Beta}[1.3,1.2] \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the expectation of $-4.3 x^2-1.2 x-1.1$ where $x \\sim \\beta(1.3,1.2)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the mean of {-10, 4, -6, -7, 4, 10}. [embedded]\n \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the mean of $\\{-10, 4, -6, -7, 4, 10 \\}$. [embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the probability that $-2.02 < 4.9\\, -4.6 x < -1.77$ where $x \\sim $ \\text{NormalDistribution}[0.,3.]. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the probability that $-2.02 < 4.9 ~ - 4.6x < -1.77$ where $x \\sim \\mathcal{N}(0,3)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the mode of {43/7, 39/7, -41/7, 61/7, 6/7}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the mode of $\\{\\frac{43}{7}, \\frac{39}{7}, -\\frac{41}{7}, \\frac{61}{7}, \\frac{6}{7} \\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Sort {-4, 2.7, -8, 27/4, -4, -1, 3 sqrt(5), 8}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Sort $\\{-4, 2.7, -8, \\frac{27}{4}, -4, -1, 3 \\sqrt{5}, 8 \\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Determine the KL Divergence between the empirical distributions {0.085,0.397,0.377} and {0.164,0.18,0.474}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Determine the KL Divergence between the empirical distributions $\\{0.085,0.397,0.377\\}$ and $\\{0.164,0.180,0.474\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the median of {4 sqrt(2), 0, 2, -2, 7, 2 sqrt(5), 3^2, -8/sqrt(3)}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the median of $\\{4 \\sqrt{2}, 0, 2, -2, 7, 2 \\sqrt{5}, 3 \\sqrt{2}, -\\frac{8}{\\sqrt{3}\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the union of the following sets, namely ${5, 12 \\log (2), 4, -\\frac{9}{\\sqrt{2}, -8.906, 8, -1} \\cup {-\\frac{9}{\\sqrt{2}, 4, 8, 12 \\log (2), -6, -3, -1, -8.288}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the union of the following sets, namely $\\{5, 12 \\log (2), 4, -\\frac{9}{\\sqrt{2}, -8.906, 8, -1\\} \\cup \\{-\\frac{9}{\\sqrt{2}, 4, 8, 12 \\log (2), -6, -3, -1, -8.288\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the mean of {3 ln (2), 7 log (2), 2 log (2), 13 log (2), -13 log (2), 7 ln (2), 14 log (2), 7 ln (2)}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the mean of ${3 \\ln (2), 7 \\log (2), 2 \\log (2), 13 \\log (2), -13 \\log (2), 7 \\ln (2), 14 \\log (2), 7 \\ln (2)}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the harmonic mean of the set ${7, 18, 17, 6}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the harmonic mean of the set $\\{7, 18, 17, 6\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the difference between two sets, namely ${-\\frac{11}{\\sqrt{3}, 8, e, \\frac{64}{7}, -5.24} \\setminus {1, \\frac{24}{7}, -5.24, \\frac{3}{2}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the difference between two sets, namely $\\{-\\frac{11}{\\sqrt{3}, 8, e, \\frac{64}{7}, -5.24\\}$ and $\\{1, \\frac{24}{7}, -5.24, \\frac{3}{2}\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the mode of ${-6, 2, 5, 6, -6, -6, 6, 6, -6, -6, 6, 6, -6, -1, -6, 2, -6, 6, -1, -1, -1, 2, 2}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the mode of $\\{-6, 2, 5, 6, -6, -6, 6, 6, -6, -6, 6, 6, -6, -1, -6, 2, -6, 6, -1, -1, -1, 2, 2\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the geometric mean of ${1, 25, 16}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the geometric mean of $\\{1, 25, 16\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the intersection of the following sets, namely ${-1, 8, 10, 4, -9} \\cap {4, -9, 8, 0, 7, -1, 1}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the intersection of the following sets, namely $\\{-1, 8, 10, 4, -9\\} \\cap \\{4, -9, 8, 0, 7, -1, 1\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the range of {-10, 9, -1, -3, -10, -8, -17/2, 2}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the range of $\\{-10, 9, -1, -3, -10, -8, -\\frac{17}{2}, 2\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the sample standard deviation of ${3, 6, 6}$.\n[embedded]\n \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the sample standard deviation of $\\{3, 6, 6\\}$.\n[embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the sample variance of ${-5, 15, 13, 2}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the sample variance of $\\{-5, 15, 13, 2\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the range of {pi, 9, 9/2, -5/sqrt(pi), 10, 6}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the range of $\\{ \\pi, 9, \\frac{9}{2}, -\\frac{5}{\\sqrt{\\pi}, 10, 6 \\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the geometric mean of ${9, 9}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the geometric mean of $\\{9, 9\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the median of {-11/2, 5, -3, -9, -3, -7, 0}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the median of $\\{-\\frac{11}{2}, 5, -3, -9, -3, -7, 0\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Convert $\\text{2hw}_{33}$ to base 10. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Convert $2 \\times \\rm{hw}_{33}$ to base $10$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Is the following number prime?\n96463 \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Is the following number prime?\n$96463$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Return up to the first 10 primitive roots of $20369$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Return up to the first $10$ primitive roots of $20369$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the $x,y,z$ such that\n$-8 x+9 y-3 z=-4$\n$x+8 y-6 z=4$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the $x,y,z$ such that\n$-8 x+9 y-3 z=-4$\n$x+8 y-6 z=4$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Factor $3646$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Factor $3646$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Factor $19535$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Factor $19535$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the modular multiplicative inverse $x$, or $x$ such that $626x \\equiv 1 \\pmod{909}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the modular multiplicative $x^{-1}$, or $x$ such that $626x \\equiv 1 \\pmod{909}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Simplify $1610^1476 \\pmod{2374}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Simplify $1610^{1476} \\mod 2374$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Is the following number prime?\n35383 \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Is the following number prime?\n$35383$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the Euler totient function $\\beta(47146)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the Euler totient function $\\phi(47146)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the greatest common divisor of complex numbers {711-878j,320+232j}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the greatest common divisor of complex numbers $\\{711-878i, 320+232i\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Convert 4301 to base $23$. [embedded]\n\n[embedded] \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Convert $4301$ to base $23$. [embedded]\n\n  \n\n[embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Are the following numbers relatively prime (coprime)? {621,157,481}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Are the following numbers relatively prime (coprime)? $\\{621,157,481\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Are the following numbers relatively prime (coprime)? {-977,351}. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Are the following numbers relatively prime (coprime)? $\\{-977, 351\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the Euler totient function $\\beta(3645)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the Euler totient function $\\phi(3645)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the least common multiple of complex numbers $\\left\\{-1- k,-\\frac{2}{5}+2k,1-2k\\right\\}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the least common multiple of complex numbers $\\left\\{-1- i,-\\frac{2}{5}+2i,1-2i\\right\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Determine whether 288 is divisible by 3.\n\n[embedded] \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Determine whether $228$ is divisible by $3$.\n\n[embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 16 \\pmod{9}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the smallest $x$ such that\n$x \\equiv 14 \\pmod{7}$\n$x \\equiv 16 \\pmod{9}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: If $x = \\frac{41098}{32823}$, then find $\\frac{1}{x+\\frac{1}{x+\\frac{1}{x+\\ddots}}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "If $x = \\frac{41098}{32823}$, then find $\\frac{1}{x+\\frac{1}{x+\\frac{1}{x+\\ddots}}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the least common multiple of $\\{13,-94\\}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the least common multiple of $\\{13,-94\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the smallest $x$ such that $x \\equiv 35557 \\pmod{18}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the smallest $x$ such that $x \\equiv 35557 \\pmod{18}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the greatest common divisor of $\\{659,838\\}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the greatest common divisor of $\\{659,838\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Determine the $n=8$ $40$-gonal number. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Determine the $n=8$ $40$-gonal number.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: A polygon with $6$ vertices has the coordinates \n$$\n\\left(\n\\begin{array}{cc}\n 0.048 & 0.456 \\\\\n 0.095 & 0.224 \\\\\n 0.118 & 0.323 \\\\\n 0.577 & 0.497 \\\\\n 0.721 & 0.185 \\\\\n 0.723 & 0.612 \\\\\n\\end{array}\n\\right)\n$$\nEstimate the polygon's interior angles (in radians), area, and perimeter. Also, classify the polygon as 'Simple' or 'Convex'. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "A polygon with $6$ vertices has the coordinates \n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n 0.048 & 0.456 \\\\\n 0.095 & 0.224 \\\\\n 0.118 & 0.323 \\\\\n 0.577 & 0.497 \\\\\n 0.721 & 0.185 \\\\\n 0.723 & 0.612 \\\\\n\\end{array}\n\\right)\n$$ \nEstimate the polygon's interior angles (in $\\rm{rad}$), area, and perimeter. Also, classify the polygon as 'Simple' or 'Convex'.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: A triangle has angle $\\frac{11 \\pi }{12}$, a side of length $4$ and an angle of measure $\\frac{\\pi }{36}$. Determine the locations of the triangle's vertices and the three interior angles. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "A triangle has angle $\\frac{11 \\pi }{12}$, a side of length $4$, and an angle of measure $\\frac{\\pi }{36}$. Determine the locations of the triangle's vertices and the three interior angles.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: A polyhedron has vertices with the coordinates \n$$\n\\left(\n\\begin{array}{ccc}\n 0.714 & 0.581 & 0.689 \\\\\n 0.786 & 0.542 & 0.532 \\\\\n 0.19 & 0.398 & 0.73 \\\\\n 0.128 & 0.212 & 0.188 \\\\\n 0.426 & 0.841 & 0.785 \\\\\n 0.524 & 0.064 & 0.883 \\\\\n 0.007 & 0.379 & 0.305 \\\\\n 0.989 & 0.341 & 0.174 \\\\\n 0.257 & 0.203 & 0.135 \\\\\n\\end{array}\n\\right)\n$$\n\nEstimate the polyhedron's surface area, volume, and the solid angle at the first listed point p spanned by edges with common point p. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "A polyhedron has vertices with the coordinates\n$$\n\\left(\n\\begin{array}{ccc}\n 0.714 & 0.581 & 0.689 \\\\\n 0.786 & 0.542 & 0.532 \\\\\n 0.19 & 0.398 & 0.73 \\\\\n 0.128 & 0.212 & 0.188 \\\\\n 0.426 & 0.841 & 0.785 \\\\\n 0.524 & 0.064 & 0.883 \\\\\n 0.007 & 0.379 & 0.305 \\\\\n 0.989 & 0.341 & 0.174 \\\\\n 0.257 & 0.203 & 0.135 \\\\\n\\end{array}\n\\right)\n$$\n\nEstimate the polyhedron's surface area, volume, and the solid angle at the first listed point $p$ spanned by edges with common point $p$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the rank of\n$$\n\\left(\n\\begin{array}{c}\n \\frac{37}{4} \\\\\n \\frac{91}{16} \\\\\n \\frac{23}{4} \\\\\n -\\frac{53}{16} \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the rank of\n$$\n\\left(\n\\begin{array}{c}\n \\frac{37}{4} \\\\\n \\frac{91}{16} \\\\\n \\frac{23}{4} \\\\\n -\\frac{53}{16} \\\\\n\\end{array}\n\\right)\n$$",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the dot product of the following two vectors $g$ and $f$:\n$\\left( \\begin{array}{c} -3 \\\\ -9 \\\\ -7 \\\\ 0 \\\\ -2 \\\\ 5 \\\\ -4 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 0 \\\\ -8 \\\\ -7 \\\\ -1 \\\\ 4 \\\\ 8 \\\\ \\end{array} \\right) $ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the dot product of the following two vectors $g$ and $f$:\n$\\left( \\begin{array}{c} -3 \\\\ -9 \\\\ -7 \\\\ 0 \\\\ -2 \\\\ 5 \\\\ -4 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 0 \\\\ -8 \\\\ -7 \\\\ -1 \\\\ 4 \\\\ 8 \\\\ \\end{array} \\right) $\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the plane defined by the following points:\n${\\left\\{\\frac{1}{2},3,-\\frac{1}{2}\\right\\}, \\left\\{-4,\\frac{1}{2},-\\frac{9}{2}\\right\\}, \\left\\{-\\frac{5}{2},\\frac{5}{2},-\\frac{3}{2}\\right\\}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the plane defined by the following points:\n${\\left\\{\\frac{1}{2},3,-\\frac{1}{2}\\right\\}, \\left\\{-4,\\frac{1}{2},-\\frac{9}{2}\\right\\}, \\left\\{-\\frac{5}{2},\\frac{5}{2},-\\frac{3}{2}\\right\\}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the eigenvectors of the following matrix (round your answer to three decimal places):\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{25}{3} & \\frac{17}{3} & \\frac{11}{3} \\\\\n -\\frac{29}{3} & \\frac{19}{3} & \\frac{25}{3} \\\\\n \\frac{11}{3} & -9 & -\\frac{29}{3} \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the eigenvectors of the following matrix (round your answer to three decimal places):\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{25}{3} & \\frac{17}{3} & \\frac{11}{3} \\\\\n -\\frac{29}{3} & \\frac{19}{3} & \\frac{25}{3} \\\\\n \\frac{11}{3} & -9 & -\\frac{29}{3} \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the eigenvectors of the following matrix:\n$$\n\\left(\n\\begin{array}{cc}\n \\frac{24}{5} & -\\frac{46}{5} \\\\\n -\\frac{28}{5} & \\frac{26}{5} \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the eigenvectors of the following matrix:\n$$\n\\left(\n\\begin{array}{cc}\n \\frac{24}{5} & -\\frac{46}{5} \\\\\n -\\frac{28}{5} & \\frac{26}{5} \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Subtract the second matrix from the first:\n$ \\left( \\begin{array}{ccc} 4 & -10 & -5 \\\\ 0 & -9 & 0 \\\\ 7 & 9 & 0 \\\\ \\end{array} \\right)$ from $\\left( \\begin{array}{ccc} -7 & 1 & 0 \\\\ 1 & -3 & -2 \\\\ -1 & -9 & 1 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Subtract the second matrix from the first:\n$ \\left( \\begin{array}{ccc} 4 & -10 & -5 \\\\ 0 & -9 & 0 \\\\ 7 & 9 & 0 \\\\ \\end{array} \\right)$ from $\\left( \\begin{array}{ccc} -7 & 1 & 0 \\\\ 1 & -3 & -2 \\\\ -1 & -9 & 1 \\\\ \\end{array} \\right)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Multiply\n$\\left( \\begin{array}{ccccc} -3 & -3 & 1 & 1 & 0 \\\\ 2 & 1 & -2 & -2 & 1 \\\\ 2 & 0 & -2 & -2 & 2 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -3 \\\\ -1 \\\\ -2 \\\\ -2 \\\\ -2 \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Multiply\n$\\left( \\begin{array}{ccccc} -3 & -3 & 1 & 1 & 0 \\\\ 2 & 1 & -2 & -2 & 1 \\\\ 2 & 0 & -2 & -2 & 2 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -3 \\\\ -1 \\\\ -2 \\\\ -2 \\\\ -2 \\\\ \\end{array} \\right)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Convert the following matrix to reduced row echelon form:\n$$\n\\left(\n\\begin{array}{cccc}\n 8 & -3 & -2 & 7 \\\\\n 10 & -4 & -10 & 7 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Convert the following matrix to reduced row echelon form:\n$$\n\\left(\n\\begin{array}{cccc}\n 8 & -3 & -2 & 7 \\\\\n 10 & -4 & -10 & 7 \\\\\n\\end{array}\n\\right)\n$$",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the characteristic polynomial of the following matrix:\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{49}{16} & \\frac{57}{16} & \\frac{115}{16} \\\\\n -\\frac{21}{8} & -\\frac{13}{4} & \\frac{109}{16} \\\\\n \\frac{13}{4} & \\frac{123}{16} & \\frac{9}{16} \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the characteristic polynomial of the following matrix:\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{49}{16} & \\frac{57}{16} & \\frac{115}{16} \\\\\n -\\frac{21}{8} & -\\frac{13}{4} & \\frac{109}{16} \\\\\n \\frac{13}{4} & \\frac{123}{16} & \\frac{9}{16} \\\\\n\\end{array}\n\\right)$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the distance between the following two vectors $a$ and $b$:\n$\\left( \\begin{array}{c} 9 \\\\ 4 \\\\ -3 \\\\ -7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 4 \\\\ -1 \\\\ -1 \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the distance between the following two vectors $\\bf{a}$ and $\\bf{b}$:\n$\\left( \\begin{array}{c} 9 \\\\ 4 \\\\ -3 \\\\ -7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 4 \\\\ -1 \\\\ -1 \\\\ \\end{array} \\right)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the projection of the first vector $a$ onto the second $b$:\n$\\left( \\begin{array}{c} -\\frac{1}{5} \\\\ -\\frac{1}{5} \\\\ -\\frac{8}{5} \\\\ \\frac{1}{5} \\\\ \\end{array} \\right)$, $\\left( \\begin{array}{c} \\frac{6}{5} \\\\ -2 \\\\ \\frac{3}{5} \\\\ -\\frac{14}{5} \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the projection of the first vector $\\bf{a}$ onto the second $\\bf{b}$:\n$\\left( \\begin{array}{c} -\\frac{1}{5} \\\\ -\\frac{1}{5} \\\\ -\\frac{8}{5} \\\\ \\frac{1}{5} \\\\ \\end{array} \\right)$, $\\left( \\begin{array}{c} \\frac{6}{5} \\\\ -2 \\\\ \\frac{3}{5} \\\\ -\\frac{14}{5} \\\\ \\end{array} \\right)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Subtract the second matrix from the first:\n$\\left( \\begin{array}{cc} -7 & -6 \\\\ 0 & 6 \\\\ \\end{array} \\right)$ - $\\left( \\begin{array}{cc} 3 & -9 \\\\ 1 & 4 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Subtract the second matrix from the first:\n$\\left( \\begin{array}{cc} -7 & -6 \\\\ 0 & 6 \\\\ \\end{array} \\right)$ - $\\left( \\begin{array}{cc} 3 & -9 \\\\ 1 & 4 \\\\ \\end{array} \\right)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n 1 & 1 & -4 \\\\\n -3 & -2 & -4 \\\\\n -3 & -1 & -3 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n 1 & 1 & -4 \\\\\n -3 & -2 & -4 \\\\\n -3 & -1 & -3 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):\n$$\n\\left(\n\\begin{array}{ccc}\n 6 & -4 & -4 \\\\\n -9 & 4 & 1 \\\\\n -8 & -2 & 0 \\\\\n 5 & -10 & 9 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):\n$$\n\\left(\n\\begin{array}{ccc}\n 6 & -4 & -4 \\\\\n -9 & 4 & 1 \\\\\n -8 & -2 & 0 \\\\\n 5 & -10 & 9 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the distance from the point ${-\\frac{10}{3}, -\\frac{13}{3}, -\\frac{5}{3}$ to the plane $-\\frac{7 x}{3}-\\frac{2 y}{3}-\\frac{4 z}{3}+\\frac{7}{3}=0$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the distance from the point ${-\\frac{10}{3}, -\\frac{13}{3}, -\\frac{5}{3}$ to the plane $-\\frac{7 x}{3}-\\frac{2 y}{3}-\\frac{4 z}{3}+\\frac{7}{3}=0$.",
"role": "assistant"
}
] |
[
{
"content": "Statement: Normalize the following vector $d$:\n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Normalize the following vector $\\bf{d}$: \n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)$$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Orthogonalize the following sets:\n${\\{0,2,-1\\}, \\{0,-1,3\\}, \\left\\{-\\frac{3}{2},\\frac{5}{2},-\\frac{5}{2}\\right\\}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Orthogonalize the following sets:\n${\\{0,2,-1\\}, \\{0,-1,3\\}, \\left\\{-\\frac{3}{2},\\frac{5}{2},-\\frac{5}{2}\\right\\}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{43}{16} & -\\frac{65}{16} & -\\frac{59}{16} \\\\\n -\\frac{19}{8} & -\\frac{79}{16} & -\\frac{29}{16} \\\\\n -\\frac{15}{4} & \\frac{5}{16} & -\\frac{73}{16} \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{43}{16} & -\\frac{65}{16} & -\\frac{59}{16} \\\\\n -\\frac{19}{8} & -\\frac{79}{16} & -\\frac{29}{16} \\\\\n -\\frac{15}{4} & \\frac{5}{16} & -\\frac{73}{16} \\\\\n\\end{array}\n\\right)$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the determinant of the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{3}{2} & -5 & -4 \\\\\n \\frac{9}{2} & 3 & -5 \\\\\n -\\frac{1}{2} & 5 & -4 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the determinant of the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{3}{2} & -5 & -4 \\\\\n \\frac{9}{2} & 3 & -5 \\\\\n -\\frac{1}{2} & 5 & -4 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Add the two matrices\n$ \\left( \\begin{array}{cc} -1 & -4 \\\\ 6 & -1 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{cc} -3 & 8 \\\\ 4 & -3 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Add the two matrices\n$ \\left( \\begin{array}{cc} -1 & -4 \\\\ 6 & -1 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{cc} -3 & 8 \\\\ 4 & -3 \\\\ \\end{array} \\right)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Multiply the scalar $\\frac{13}{6}$ and the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 9 & 3 & -3 \\\\\n -5 & -5 & -5 \\\\\n -7 & -3 & 1 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Multiply the scalar $\\frac{13}{6}$ and the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 9 & 3 & -3 \\\\\n -5 & -5 & -5 \\\\\n -7 & -3 & 1 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute\n\n  \n\n$$\ne^\\left(\n\\begin{array}{cc}\n 1 & -1 \\\\\n 1 & -1 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute\n\n  \n\n$$\ne^\\left(\n\\begin{array}{cc}\n 1 & -1 \\\\\n 1 & -1 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Give a list of vectors that forms a basis for the null space of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 4 & 7 & 3 \\\\\n -4 & 5 & -7 \\\\\n 9 & 8 & -4 \\\\\n 4 & 4 & -1 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Give a list of vectors that forms a basis for the null space of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 4 & 7 & 3 \\\\\n -4 & 5 & -7 \\\\\n 9 & 8 & -4 \\\\\n 4 & 4 & -1 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the cross product of the following vectors $a$ and $g$:\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the cross product of the following vectors $\\bf{a}$ and $\\bf{g}$:\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Multiply the scalar $-\\frac{7}{4}$ and the matrix\n\n  \n\n$$\n\\left( \\begin{array}{cccc}\n -8 & 3 & -1 & 0 \\\\\n 8 & -6 & 8 & -6 \\\\\n -6 & -6 & 1 & -6 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded] \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Multiply the scalar $-\\frac{7}{4}$ and the matrix\n\n  \n\n$$\n\\left( \\begin{array}{cccc}\n -8 & 3 & -1 & 0 \\\\\n 8 & -6 & 8 & -6 \\\\\n -6 & -6 & 1 & -6 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Add the two matrices\n$\\left( \\begin{array}{c} -3 \\\\ \\frac{8}{5} \\\\ 9 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} \\frac{22}{5} \\\\ \\frac{19}{5} \\\\ \\frac{18}{5} \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Add the two matrices\n$\\left( \\begin{array}{c} -3 \\\\ \\frac{8}{5} \\\\ 9 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} \\frac{22}{5} \\\\ \\frac{19}{5} \\\\ \\frac{18}{5} \\\\ \\end{array} \\right)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the trace of\n\n  \n\n$$\n\\left(\n\\begin{array}{cccc}\n 6 & 1 & -10 & -7 \\\\\n -10 & 4 & -8 & 1 \\\\\n -8 & -9 & 1 & 9 \\\\\n -10 & 8 & -7 & 3 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded] \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Compute the trace of\n\n  \n\n$$\n\\left(\n\\begin{array}{cccc}\n 6 & 1 & -10 & -7 \\\\\n -10 & 4 & -8 & 1 \\\\\n -8 & -9 & 1 & 9 \\\\\n -10 & 8 & -7 & 3 \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the characteristic polynomial of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -3 & -\\frac{4}{5} \\\\\n -\\frac{3}{5} & \\frac{18}{5} \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded] \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the characteristic polynomial of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -3 & -\\frac{4}{5} \\\\\n -\\frac{3}{5} & \\frac{18}{5} \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded]\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the least squares vector given the matrix\n$\\mathbf{A} = \\left( \\begin{array}{cc} 1 & 1 \\\\ 0 & -2 \\\\ 1 & -2 \\\\ -3 & 0 \\\\ \\end{array} \\right)$ and the vector $\\mathbf{b} = \\left( \\begin{array}{c} -2.65 \\\\ 2.69 \\\\ -2.86 \\\\ -0.45 \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the least squares vector given the matrix\n$\\bf{A} = \\left( \\begin{array}{cc} 1 & 1 \\\\ 0 & -2 \\\\ 1 & -2 \\\\ -3 & 0 \\\\ \\end{array} \\right)$ and the vector $\\bf{b} = \\left( \\begin{array}{c} -2.65 \\\\ 2.69 \\\\ -2.86 \\\\ -0.45 \\\\ \\end{array} \\right)$.",
"role": "assistant"
}
] |
[
{
"content": "Statement: Convert the following matrix to reduced row echelon form:\n\n  \n\n$$\n\\left(\n\\begin{array}{ccccc}\n 10 & -8 & 6 & 0 & -1 \\\\\n -1 & 1 & -1 & -1 & -2 \\\\\n -4 & -1 & -5 & 0 & -10 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Convert the following matrix to reduced row echelon form:\n\n  \n\n$$\n\\left(\n\\begin{array}{ccccc}\n 10 & -8 & 6 & 0 & -1 \\\\\n -1 & 1 & -1 & -1 & -2 \\\\\n -4 & -1 & -5 & 0 & -10 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the dot product of the following two vectors m and n:\n$\\left( \\begin{array}{c} 3 \\sqrt{2} \\\\ -6 \\sqrt{2} \\\\ -\\sqrt{2} \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -\\sqrt{2} \\\\ 0 \\\\ -\\frac{9}{\\sqrt{2} \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the dot product of the following two vectors $\\bf{m}$ and $\\bf{n}$:\n$\\left( \\begin{array}{c} 3 \\sqrt{2} \\\\ -6 \\sqrt{2} \\\\ -\\sqrt{2} \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -\\sqrt{2} \\\\ 0 \\\\ -\\frac{9}{\\sqrt{2} \\\\ \\end{array} \\right)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Multiply\n$\\left( \\begin{array}{ccc} 1 & 2 & 0 \\\\ -2 & 2 & -2 \\\\ -2 & -1 & 0 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{ccc} -3 & 2 & -1 \\\\ -1 & 2 & 2 \\\\ -1 & -1 & 2 \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Multiply\n$\\left( \\begin{array}{ccc} 1 & 2 & 0 \\\\ -2 & 2 & -2 \\\\ -2 & -1 & 0 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{ccc} -3 & 2 & -1 \\\\ -1 & 2 & 2 \\\\ -1 & -1 & 2 \\\\ \\end{array} \\right)$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the determinant of the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{7}{6} & \\frac{23}{6} & -\\frac{23}{6} \\\\\n -2 & -\\frac{1}{3} & -\\frac{11}{6} \\\\\n \\frac{5}{3} & \\frac{14}{3} & \\frac{3}{2} \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the determinant of the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{7}{6} & \\frac{23}{6} & -\\frac{23}{6} \\\\\n -2 & -\\frac{1}{3} & -\\frac{11}{6} \\\\\n \\frac{5}{3} & \\frac{14}{3} & \\frac{3}{2} \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the $\\ell_\\infty$ norm of the following vector $y$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the $\\ell_\\infty$ norm of the following vector $\\bf{y}$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the eigenvalues of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -\\frac{20}{3} & \\frac{11}{3} \\\\\n -7 & 8 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the eigenvalues of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -\\frac{20}{3} & \\frac{11}{3} \\\\\n -7 & 8 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the eigenvalues of the following matrix (round your answer to three decimal places):\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -1 & 9 & 8 \\\\\n 1 & 10 & 2 \\\\\n 8 & -8 & -9 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the eigenvalues of the following matrix (round your answer to three decimal places):\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -1 & 9 & 8 \\\\\n 1 & 10 & 2 \\\\\n 8 & -8 & -9 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the $\\ell_2$ norm of the following vector $x$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n 1 \\\\\n -8 \\\\\n -7 \\\\\n -6 \\\\\n -4 \\\\\n 0 \\\\\n -6 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the $\\ell_2$ norm of the following vector $\\bf{x}$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n 1 \\\\\n -8 \\\\\n -7 \\\\\n -6 \\\\\n -4 \\\\\n 0 \\\\\n -6 \\\\\n\\end{array}\n\\right)\n$$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the cross product of the following vectors $p$ and $q$:\n$\\left( \\begin{array}{c} -\\frac{39}{5} \\\\ \\frac{31}{10} \\\\ -\\frac{67}{10} \\\\ \\end{array}\n\\right)$ and $\\left( \\begin{array}{c} \\frac{9}{10} \\\\ \\frac{43}{5} \\\\ 3 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the cross product of the following vectors $\\bf{p}$ and $\\bf{q}$:\n$\\left( \\begin{array}{c} -\\frac{39}{5} \\\\ \\frac{31}{10} \\\\ -\\frac{67}{10} \\\\ \\end{array}\n\\right)$ and $\\left( \\begin{array}{c} \\frac{9}{10} \\\\ \\frac{43}{5} \\\\ 3 \\\\ \\end{array} \\right)$",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the gradient of the function f(x,y,z) where $f(x,y,z) = x^3$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the gradient of the function $f(x,y,z)$ where $f(x,y,z) = x^3$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the laplacian of the function $f(x,y,z)$ where $f(x,y,z) = \\sqrt{\\frac{x}{y z}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the Laplacian of the function $f(x,y,z)$ where $f(x,y,z) = \\sqrt{\\frac{x}{yz}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the arclength of the function $f(x) = \\cosh (5x)$ on the interval $x = 4$ to $x = 4$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the arclength of the function $f(x) = \\cosh (5x)$ on the interval $x = 4$ to $x = 4$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Differentiate the following function:\n$\\cos (4 x+9)-\\cos (8-2 x)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Differentiate the following function:\n$\\cos (4 x+9)-\\cos (8-2 x)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the jacobian of the vector valued function $\\begin{pmatrix} f(x,y,z)\\\\ g(x,y,z) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(x,y,z) = \\sin (x)$, $g(x,y,z) = \\tan (y+z)$, and $h(x,y,z) = \\frac{1}{z^2}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the Jacobian of the vector-valued function $\\begin{pmatrix} f(x,y,z)\\\\ g(x,y,z) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(x,y,z) = \\sin(x)$, $g(x,y,z) = \\tan(y+z)$, and $h(x,y,z) = \\frac{1}{z^2}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Differentiate the following function:\n$e^{2 x^2+6}+\\log (4-2 x)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Differentiate the following function:\n$e^{2 x^2+6}+\\log (4-2 x)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the divergence of the vector field $l = \\uvec{h} + g(x,y,z)\\uvec{j} + h(x,y,z)\\uvec{k}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the divergence of the vector field $\\bf{l} = \\hat{\\bf{i} + g(x,y,z)\\hat{\\bf{j} + h(x,y,z)\\hat{\\bf{k}$",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the second derivative of the following function:\n$e^{8 x-7}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the second derivative of the following function:\n$e^{8x-7}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the curl of the vector field $p = \\uvec{i} + g(x,y,z)\\uvec{g} + h(x,y,z)\\uvec{y}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the curl of the vector field $\\bf{p} = \\hat{\\bf{i} + g(x,y,z)\\hat{\\bf{j} + h(x,y,z)\\hat{\\bf{k}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find an indefinite integral (which can vary by a constant) of the following function:\n$\\frac{x^2 \\left(64 x \\left(x^3+2\\right) \\cot \\left(1-8 x^4\\right)+3\\right) \\csc \\left(1-8 x^4\\right)}{\\sqrt{2} \\sqrt{-x^3-2}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find an indefinite integral (which can vary by a constant) of the following function:\n$\\frac{x^2 \\left(64 x \\left(x^3+2\\right) \\cot \\left(1-8 x^4\\right)+3\\right) \\csc \\left(1-8 x^4\\right)}{\\sqrt{2} \\sqrt{-x^3-2}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: \n[embedded]\n\n  \n\nFind the first order expansion about $x = -1$ of the composition $f(g(x))$ for $f(x) = e^{x^2}$ and $g(t) = $e^x$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "[embedded]\n\n  \n\nFind the first order expansion about $x = -1$ of the composition$f(g(x))$ for $f(x) = e^{x^2}$ and $g(x) = e^x$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the second order series of the inverse of the following function around 2:\n$\\frac{9 x^2}{4}-e^{-7 x/2}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the second order series of the inverse of the following function around $2$:\n$\\frac{9x^2}{4}-e^{-\\frac{7x}{2}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the range of the following function:\n$\\cos (5 x+6)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the range of the following function:\n$\\cos(5x + 6)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the domain of the following function:\n$\\log (-2 x-5)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Find the domain of the following function:\n$\\log(-2x-5)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Simplify $\\frac{\\left(\\left(\\frac{21}{2}+8\\right)^2-2\\right)-18}{((11-15)-6)+15}$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form of the equations or transform the equations. Strictly just express your answer as 'The revised statement is...'. Do not explain",
"role": "user"
},
{
"content": "Simplify $\\frac{\\left(\\left(\\frac{21}{2}+8\\right)^2-2\\right)-18}{((11-15)-6)+15}$.\n",
"role": "assistant"
}
] |
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