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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... |
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"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 th... |
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"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 ju... |
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"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 t... |
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"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 exp... |
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"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... |
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"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... |
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"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 equa... |
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"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 LaTe... |
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"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 ... |
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"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 ... |
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"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 th... |
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"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 eq... |
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"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 yo... |
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"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 equ... |
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"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 ju... |
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"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. S... |
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"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 expre... |
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{
"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 ... |
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{
"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 an... |
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{
"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 ex... |
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"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 ans... |
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"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 answ... |
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"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 e... |
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"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... |
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"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 stat... |
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"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 sta... |
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"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 tr... |
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{
"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 ... |
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"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 answ... |
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{
"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 exp... |
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"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 equatio... |
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"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 exp... |
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"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. ... |
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"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. Str... |
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{
"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 expr... |
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"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 equatio... |
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"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 ... |
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"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 ... |
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"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 tran... |
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"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 expre... |
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"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. Strictl... |
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"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 ex... |
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"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 ans... |
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"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... |
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"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 cor... |
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"content": "Statement: A polyhedron has vertices with the coordinates \n$$\n\\left(\n\\begin{array}{ccc}\n 0.714 & 0.581 & 0.689 \\\\\n 0.786 & 0.542 & 0.532 \\\\\n 0.19 & 0.398 & 0.73 \\\\\n 0.128 & 0.212 & 0.188 \\\\\n 0.426 & 0.841 & 0.785 \\\\\n 0.524 & 0.064 & 0.883 \\\\\n 0.007 & 0.379 & 0.305 \\\\\n 0.... |
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"content": "Statement: Compute the rank of\n$$\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$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex withou... |
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"content": "Statement: Find the dot product of the following two vectors $g$ and $f$:\n$\\left( \\begin{array}{c} -3 \\\\ -9 \\\\ -7 \\\\ 0 \\\\ -2 \\\\ 5 \\\\ -4 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 0 \\\\ -8 \\\\ -7 \\\\ -1 \\\\ 4 \\\\ 8 \\\\ \\end{array} \\right) $ \nTas... |
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"content": "Statement: Find the plane defined by the following points:\n${\\left\\{\\frac{1}{2},3,-\\frac{1}{2}\\right\\}, \\left\\{-4,\\frac{1}{2},-\\frac{9}{2}\\right\\}, \\left\\{-\\frac{5}{2},\\frac{5}{2},-\\frac{3}{2}\\right\\}$. \nTask: Propose a corrected statement that uses common variable, convention... |
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"content": "Statement: Find the eigenvectors of the following matrix (round your answer to three decimal places):\n$$\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... |
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"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 unit... |
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"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 s... |
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"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... |
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"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 with... |
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"content": "Statement: Find the characteristic polynomial of the following matrix:\n$$\n\\left(\n\\begin{array}{ccc}\n \\frac{49}{16} & \\frac{57}{16} & \\frac{115}{16} \\\\\n -\\frac{21}{8} & -\\frac{13}{4} & \\frac{109}{16} \\\\\n \\frac{13}{4} & \\frac{123}{16} & \\frac{9}{16} \\\\\n\\end{array}\n\\right)\... |
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"content": "Statement: Find the distance between the following two vectors $a$ and $b$:\n$\\left( \\begin{array}{c} 9 \\\\ 4 \\\\ -3 \\\\ -7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -7 \\\\ 4 \\\\ -1 \\\\ -1 \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses c... |
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"content": "Statement: Find the projection of the first vector $a$ onto the second $b$:\n$\\left( \\begin{array}{c} -\\frac{1}{5} \\\\ -\\frac{1}{5} \\\\ -\\frac{8}{5} \\\\ \\frac{1}{5} \\\\ \\end{array} \\right)$, $\\left( \\begin{array}{c} \\frac{6}{5} \\\\ -2 \\\\ \\frac{3}{5} \\\\ -\\frac{14}{5} \\\\ ... |
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"content": "Statement: Subtract the second matrix from the first:\n$\\left( \\begin{array}{cc} -7 & -6 \\\\ 0 & 6 \\\\ \\end{array} \\right)$ - $\\left( \\begin{array}{cc} 3 & -9 \\\\ 1 & 4 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and... |
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"content": "Statement: Compute the (pseudo)inverse of\n$$\n\\left(\n\\begin{array}{ccc}\n 1 & 1 & -4 \\\\\n -3 & -2 & -4 \\\\\n -3 & -1 & -3 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing t... |
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"content": "Statement: Give a list of vectors that forms a basis for the null space of the following matrix (round your answer to three decimal places):\n$$\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$$ \nTask: Propose a co... |
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"content": "Statement: Find the distance from the point ${-\\frac{10}{3}, -\\frac{13}{3}, -\\frac{5}{3}$ to the plane $-\\frac{7 x}{3}-\\frac{2 y}{3}-\\frac{4 z}{3}+\\frac{7}{3}=0$. \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraph... |
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"content": "Statement: Normalize the following vector $d$:\n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the form... |
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"content": "Statement: Orthogonalize the following sets:\n${\\{0,2,-1\\}, \\{0,-1,3\\}, \\left\\{-\\frac{3}{2},\\frac{5}{2},-\\frac{5}{2}\\right\\}$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modi... |
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"content": "Statement: Compute the (pseudo)inverse of\n$$\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$$ \nTask: Propose a cor... |
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"content": "Statement: Find the determinant of the matrix\n\n  \n\n$$\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$$ \nTask: Propose a corrected statement that uses common variable, conventional nota... |
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"content": "Statement: Add the two matrices\n$ \\left( \\begin{array}{cc} -1 & -4 \\\\ 6 & -1 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{cc} -3 & 8 \\\\ 4 & -3 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units i... |
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"content": "Statement: Multiply the scalar $\\frac{13}{6}$ and the matrix\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n 9 & 3 & -3 \\\\\n -5 & -5 & -5 \\\\\n -7 & -3 & 1 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct ... |
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"content": "Statement: Compute\n\n  \n\n$$\ne^\\left(\n\\begin{array}{cc}\n 1 & -1 \\\\\n 1 & -1 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex without paraphrasing the statement. Do not modify the fo... |
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"content": "Statement: Give a list of vectors that forms a basis for the null space of the following matrix:\n\n  \n\n$$\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$$ \nTask: Propose a corrected statement that uses c... |
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"content": "Statement: Find the cross product of the following vectors $a$ and $g$:\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, convention... |
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"content": "Statement: Multiply the scalar $-\\frac{7}{4}$ and the matrix\n\n  \n\n$$\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$$\n\n  \n\n[embedded] \nTask: Propose a corrected statement that uses common v... |
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"content": "Statement: Add the two matrices\n$\\left( \\begin{array}{c} -3 \\\\ \\frac{8}{5} \\\\ 9 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} \\frac{22}{5} \\\\ \\frac{19}{5} \\\\ \\frac{18}{5} \\\\ \\end{array} \\right)$ \nTask: Propose a corrected statement that uses common variable, con... |
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"content": "Statement: Compute the trace of\n\n  \n\n$$\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$$\n\n  \n\n[embedded] \nTask: Propose a corrected statement that uses common varia... |
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"content": "Statement: Find the characteristic polynomial of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -3 & -\\frac{4}{5} \\\\\n -\\frac{3}{5} & \\frac{18}{5} \\\\\n\\end{array}\n\\right)\n$$\n\n  \n\n[embedded] \nTask: Propose a corrected statement that uses common ... |
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"content": "Statement: Find the least squares vector given the matrix\n$\\mathbf{A} = \\left( \\begin{array}{cc} 1 & 1 \\\\ 0 & -2 \\\\ 1 & -2 \\\\ -3 & 0 \\\\ \\end{array} \\right)$ and the vector $\\mathbf{b} = \\left( \\begin{array}{c} -2.65 \\\\ 2.69 \\\\ -2.86 \\\\ -0.45 \\\\ \\end{array} \\right... |
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"content": "Statement: Convert the following matrix to reduced row echelon form:\n\n  \n\n$$\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$$ \nTask: Propose a corrected statement that uses common varia... |
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"content": "Statement: Find the dot product of the following two vectors m and n:\n$\\left( \\begin{array}{c} 3 \\sqrt{2} \\\\ -6 \\sqrt{2} \\\\ -\\sqrt{2} \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} -\\sqrt{2} \\\\ 0 \\\\ -\\frac{9}{\\sqrt{2} \\\\ \\end{array} \\right)$. \nTask: Propose ... |
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"content": "Statement: Multiply\n$\\left( \\begin{array}{ccc} 1 & 2 & 0 \\\\ -2 & 2 & -2 \\\\ -2 & -1 & 0 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{ccc} -3 & 2 & -1 \\\\ -1 & 2 & 2 \\\\ -1 & -1 & 2 \\\\ \\end{array} \\right)$. \nTask: Propose a corrected statement that uses common variable... |
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"content": "Statement: Find the determinant of the matrix\n\n  \n\n$$\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$$ \nTask: Propose a correct... |
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"content": "Statement: Find the $\\ell_\\infty$ norm of the following vector $y$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in LaTex witho... |
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{
"content": "Statement: Find the eigenvalues of the following matrix:\n\n  \n\n$$\n\\left(\n\\begin{array}{cc}\n -\\frac{20}{3} & \\frac{11}{3} \\\\\n -7 & 8 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variable, conventional notation and correct units in La... |
[
{
"content": "Statement: Find the eigenvalues of the following matrix (round your answer to three decimal places):\n\n  \n\n$$\n\\left(\n\\begin{array}{ccc}\n -1 & 9 & 8 \\\\\n 1 & 10 & 2 \\\\\n 8 & -8 & -9 \\\\\n\\end{array}\n\\right)\n$$ \nTask: Propose a corrected statement that uses common variabl... |
[
{
"content": "Statement: Find the $\\ell_2$ norm of the following vector $x$:\n\n  \n\n$$\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 a... |
[
{
"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: ... |
[
{
"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. Str... |
[
{
"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 transfo... |
[
{
"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 tr... |
[
{
"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. ... |
[
{
"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 nota... |
[
{
"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. St... |
[
{
"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 o... |
[
{
"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. St... |
[
{
"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 tran... |
[
{
"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 varia... |
[
{
"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 st... |
[
{
"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 ... |
[
{
"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 j... |
[
{
"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... |
[
{
"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 trans... |
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