formatted
listlengths 2
2
|
|---|
[
{
"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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "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'.",
"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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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.",
"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 $p$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $q$ spanned by edges with common point $q$.\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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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) $\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find the dot product of the following two vectors $a$ and $c$:\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\\}}$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find the plane defined by the following points:\n${\\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$$\n\\left(\n\\begin{array}{ccc}\n \\frac{25}{3} & \\frac{17}{3} & \\frac{11}{3} \\\\\n -\\frac{29}{3} & \\frac{19}{3} & \\frac{25}{3} \\\\\n \\frac{11}{3} & -9 & -\\frac{29}{3} \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{cc}\n \\frac{24}{5} & -\\frac{46}{5} \\\\\n -\\frac{28}{5} & \\frac{26}{5} \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\left( \\begin{array}{ccc} -7 & 1 & 0 \\\\ 1 & -3 & -2 \\\\ -1 & -9 & 1 \\\\ \\end{array} \\right)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\left( \\begin{array}{c} -3 \\\\ -1 \\\\ -2 \\\\ -2 \\\\ -2 \\\\ \\end{array} \\right)$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{d}$ and $\\bf{g}$:\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 \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{h}$ onto the second $\\bf{k}$:\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 \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\left( \\begin{array}{cc} -7 & -6 \\\\ 0 & 6 \\\\ \\end{array} \\right)$ - $\\left( \\begin{array}{cc} 3 & -9 \\\\ 1 & 4 \\\\ \\end{array} \\right)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n 1 & 1 & -4 \\\\\n -3 & -2 & -4 \\\\\n -3 & -1 & -3 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n 6 & -4 & -4 \\\\\n -9 & 4 & 1 \\\\\n -8 & -2 & 0 \\\\\n 5 & -10 & 9 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{f}$: \n$$\n\\left(\n\\begin{array}{c}\n -1 \\\\\n 2 \\\\\n\\end{array}\n\\right)$$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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${\\{0,2,-1\\}, \\{0,-1,3\\}, \\left\\{-\\frac{3}{2},\\frac{5}{2},-\\frac{5}{2}\\right\\}}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n -\\frac{3}{2} & -5 & -4 \\\\\n \\frac{9}{2} & 3 & -5 \\\\\n -\\frac{1}{2} & 5 & -4 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\left( \\begin{array}{cc} -3 & 8 \\\\ 4 & -3 \\\\ \\end{array} \\right)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n 9 & 3 & -3 \\\\\n -5 & -5 & -5 \\\\\n -7 & -3 & 1 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\ne^\\left(\n\\begin{array}{cc}\n 1 & -1 \\\\\n 1 & -1 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n 4 & 7 & 3 \\\\\n -4 & 5 & -7 \\\\\n 9 & 8 & -4 \\\\\n 4 & 4 & -1 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{q}$ and $\\bf{t}$:\n$\\left( \\begin{array}{c} -9 \\\\ 3 \\\\ 7 \\\\ \\end{array} \\right)$ and $\\left( \\begin{array}{c} 6 \\\\ 0 \\\\ 3 \\\\ \\end{array} \\right)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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]\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\left( \\begin{array}{c} \\frac{22}{5} \\\\ \\frac{19}{5} \\\\ \\frac{18}{5} \\\\ \\end{array} \\right)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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]\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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]\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\bf{h} = \\left( \\begin{array}{cc} 1 & 1 \\\\ 0 & -2 \\\\ 1 & -2 \\\\ -3 & 0 \\\\ \\end{array} \\right)$ and the vector $\\bf{g} = \\left( \\begin{array}{c} -2.65 \\\\ 2.69 \\\\ -2.86 \\\\ -0.45 \\\\ \\end{array} \\right)$. \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccccc}\n 10 & -8 & 6 & 0 & -1 \\\\\n -1 & 1 & -1 & -1 & -2 \\\\\n -4 & -1 & -5 & 0 & -10 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{z}$ and $\\bf{y}$:\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 \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\left( \\begin{array}{ccc} -3 & 2 & -1 \\\\ -1 & 2 & 2 \\\\ -1 & -1 & 2 \\\\ \\end{array} \\right)$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n \\frac{7}{6} & \\frac{23}{6} & -\\frac{23}{6} \\\\\n -2 & -\\frac{1}{3} & -\\frac{11}{6} \\\\\n \\frac{5}{3} & \\frac{14}{3} & \\frac{3}{2} \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{t}$:\n\n  \n\n$$\n\\left(\n\\begin{array}{c}\n \\frac{40}{7} \\\\\n -5 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{cc}\n -\\frac{20}{3} & \\frac{11}{3} \\\\\n -7 & 8 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$$\n\\left(\n\\begin{array}{ccc}\n -1 & 9 & 8 \\\\\n 1 & 10 & 2 \\\\\n 8 & -8 & -9 \\\\\n\\end{array}\n\\right)\n$$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{n}$:\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 \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{h}$ and $\\bf{g}$:\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: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $f(a,b,c)$ where $f(d,e,f) = x^3$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $f(y,t,w)$ where $f(y,r,a) = \\sqrt{\\frac{g}{jt}}$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $f(a) = \\cosh (5t)$ on the interval $y = 4$ to $a = 4$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\cos (4 z+9)-\\cos (8-2 z)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\begin{pmatrix} f(g,h,y)\\\\ g(y,u,h) \\\\ h(x,y,z)\\end{pmatrix}$ where $f(s,g,a) = \\sin(x)$, $g(x,h,g) = \\tan(y+z)$, and $h(x,y,z) = \\frac{1}{z^2}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$e^{2 x^2+6}+\\log (4-2 x)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{l} = \\hat{\\bf{k}} + g(x,y,z)\\hat{\\bf{g}} + h(x,y,z)\\hat{\\bf{k}}$ \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$e^{8y-7}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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 $\\bf{t} = \\hat{\\bf{e}} + g(x,y,z)\\hat{\\bf{k}} + h(a,b,c)\\hat{\\bf{h}}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\frac{t^2 \\left(64 x \\left(t^3+2\\right) \\cot \\left(1-8 t^4\\right)+3\\right) \\csc \\left(1-8 x^4\\right)}{\\sqrt{2} \\sqrt{-t^3-2}}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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: [embedded]\n\n  \n\nFind the first order expansion about $g = -1$ of the composition$r(a(h))$ for $f(x) = e^{x^2}$ and $g(x) = e^x$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\frac{9x^2}{4}-e^{-\\frac{7x}{2}}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\cos(5k + 6)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"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$\\log(-2k-5)$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find the domain of the following function:\n$\\log(-2x-5)$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Simplify $\\frac{\\left(\\left(\\frac{21}{2}+8\\right)^2-2\\right)-18}{((11-15)-6)+15}$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Simplify $\\frac{\\left(\\left(\\frac{21}{2}+8\\right)^2-2\\right)-18}{((11-15)-6)+15}$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find all real solutions to $\\frac{\\log (g+3)}{\\log (9)}+\\frac{\\log (-20 g-9)}{\\log (9)}=\\frac{\\log (g-2)}{\\log (9)}$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find all real solutions to $\\frac{\\log (x+3)}{\\log (9)}+\\frac{\\log (-20 x-9)}{\\log (9)}=\\frac{\\log (x-2)}{\\log (9)}$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Evaluate the function $f(j)=\\cos \\left(6j+\\frac{13}{2}\\right) \\tan \\left(6j+\\frac{1}{2}\\right)$ at the point $j=40$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Evaluate the function $f(x)=\\cos \\left(6x+\\frac{13}{2}\\right) \\tan \\left(6x+\\frac{1}{2}\\right)$ at the point $x=40$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Compute the following expression: $\\sum_{t=0}^5 -\\frac{12}{47}\\times 10^t$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Compute the following expression: $\\sum_{k=0}^5 -\\frac{12}{47}\\times 10^k$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Simplify the following expression $(-5 \\sqrt{2} \\left(\\frac{\\sqrt{3}}{2}+\\frac{i}{2}\\right)\\)^6$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Simplify the following expression $(-5 \\sqrt{2} \\left(\\frac{\\sqrt{3}}{2}+\\frac{i}{2}\\right)\\)^6$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Consider the arithmetic sequence defined by $a_1=\\frac{24}{11}$, and $a_u=a_{u-1}+2 \\pi$ for $u > 1$. Compute the $n$th partial sum, $S_u=\\sum_{k=1}^u a_k$, where $u=16$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Consider the arithmetic sequence defined by $a_1=\\frac{24}{11}$, and $a_n=a_{n-1}+2 \\pi$ for $n > 1$. Compute the $n$th partial sum, $S_n=\\sum_{k=1}^n a_k$, where $n=16$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find all real solutions to $ \\left| \\frac{13i}{2} - \\frac{45}{2} \\right| = 22$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find all real solutions to $ \\left| \\frac{13x}{2} - \\frac{45}{2} \\right| = 22$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find the norm and argument (phase angle in $\\rm{rad}$) of complex number $(3+3p)e$.\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find the norm and argument (phase angle in $\\rm{rad}$) of complex number $(3+3i)e$.\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Solve for $g=j(h)$ given the following parametric equations:\n\n  \n\n$g(h)=\\frac{16}{625} (51 t+625)^2, j(h)=-\\frac{6 t}{5}-15$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Solve for $y=f(x)$ given the following parametric equations:\n\n  \n\n$y(t)=\\frac{16}{625} (51 t+625)^2, x(t)=-\\frac{6 t}{5}-15$\n",
"role": "assistant"
}
] |
[
{
"content": "Statement: Find all real solutions to $\\frac{-220 z^3-384 z^2-584 z-528}{-180 z-216}=0$\n \nTask: Rewrite the statement in latex. You are only allowed to substitute notations, symbols and units. You are not allowed to change the numbers, wordings nor paraphrase. You are not allowed to add or remove notations, units and variables.",
"role": "user"
},
{
"content": "Find all real solutions to $\\frac{-220 x^3-384 x^2-584 x-528}{-180 x-216}=0$\n",
"role": "assistant"
}
] |
README.md exists but content is empty.
- Downloads last month
- -