query
stringlengths
39
221
ground_truth
stringlengths
1
59
stepwise_ground_truths
stringlengths
20
129
tools
listlengths
6
6
Evaluate the rank of matrix A = [[-68, -68, 75], [42, 58, -71], [42, -49, 17]].
3
[{"matrix_rank": 3}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix for A = [[9, -9, 6], [8, -2, 7], [-10, 10, -7]]. Step 2: find tr(B) for B = the result from step 1.
-5.0
[{"matrix_cofactor": [[-56, -14, 60], [-3, -3, 0], [-51, -15, 54]]}, {"matrix_trace": -5.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: evaluate the cofactor matrix of A = [[-6, 5], [-8, -4]]. Step 2: what is the trace of B = the result from step 1?
-10.0
[{"matrix_cofactor": [[-4, 8], [-5, -6]]}, {"matrix_trace": -10.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find A^T for A = [[-12, 80], [519, 461]]. Step 2: find the cofactor matrix for B = the result from step 1. Step 3: find rank(C) for C = the result from step 2.
2
[{"matrix_transpose": [[-12, 519], [80, 461]]}, {"matrix_cofactor": [[461, -80], [-519, -12]]}, {"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Find the cofactor matrix for A = [[-14, -2], [-12, -15]].
[[-15, 12], [2, -14]]
[{"matrix_cofactor": [[-15, 12], [2, -14]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: determine the cofactor matrix of A = [[-7, -6, -2], [-2, -2, 9], [-10, -9, 5]]. Step 2: find tr(B) for B = the result from step 1.
18.0
[{"matrix_cofactor": [[71, -80, -2], [48, -55, -3], [-58, 67, 2]]}, {"matrix_trace": 18.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Determine the trace of matrix A = [[5, -33], [-38, -14]].
-9.0
[{"matrix_trace": -9.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
What is the rank of matrix A = [[95, 138], [-133, 67]]?
2
[{"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix for A = [[4, -8], [-5, 3]]. Step 2: find tr(B) for B = the result from step 1.
7.0
[{"matrix_cofactor": [[3, 5], [8, 4]]}, {"matrix_trace": 7.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: compute the cofactor matrix of A = [[12, 9, -11], [8, -8, 8], [-11, 6, 12]]. Step 2: determine the trace of matrix B = the result from step 1.
-289.0
[{"matrix_cofactor": [[-144, -184, -40], [-174, 23, -171], [-16, -184, -168]]}, {"matrix_trace": -289.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the matrix of cofactors for A = [[7, 8], [-6, -3]]? Step 2: find the trace of matrix B = the result from step 1.
4.0
[{"matrix_cofactor": [[-3, 6], [-8, 7]]}, {"matrix_trace": 4.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix of A = [[56, 139], [-304, -115]]. Step 2: find B^T for B = the result from step 1. Step 3: find tr(C) for C = the result from step 2.
-59.0
[{"matrix_cofactor": [[-115, 304], [-139, 56]]}, {"matrix_transpose": [[-115, -139], [304, 56]]}, {"matrix_trace": -59.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the transpose of A = [[496, -274], [97, 379]]? Step 2: what is the matrix of cofactors for B = the result from step 1? Step 3: find the rank of matrix C = the result from step 2.
2
[{"matrix_transpose": [[496, 97], [-274, 379]]}, {"matrix_cofactor": [[379, 274], [-97, 496]]}, {"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the transpose of A = [[110, 29, -82], [-115, 231, 127], [-237, -4, 205]]? Step 2: calculate the Frobenius norm of matrix B = the result from step 1.
447.87
[{"matrix_transpose": [[110, -115, -237], [29, 231, -4], [-82, 127, 205]]}, {"frobenius_norm": 447.87}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Determine the cofactor matrix of A = [[-15, 4], [-11, 15]].
[[15, 11], [-4, -15]]
[{"matrix_cofactor": [[15, 11], [-4, -15]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the transpose of A = [[-224, -38], [-115, -116]]? Step 2: what is ||B||_F for B = the result from step 1?
279.82
[{"matrix_transpose": [[-224, -115], [-38, -116]]}, {"frobenius_norm": 279.82}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: determine the cofactor matrix of A = [[-11, 3, 13], [-3, 13, 2], [3, -3, -11]]. Step 2: what is the trace of B = the result from step 1?
-189.0
[{"matrix_cofactor": [[-137, -27, -30], [-6, 82, -24], [-163, -17, -134]]}, {"matrix_trace": -189.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix for A = [[-292, -129], [-264, 112]]. Step 2: find B^T for B = the result from step 1. Step 3: find the trace of matrix C = the result from step 2.
-180.0
[{"matrix_cofactor": [[112, 264], [129, -292]]}, {"matrix_transpose": [[112, 129], [264, -292]]}, {"matrix_trace": -180.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix for A = [[5, 6], [6, 3]]. Step 2: what is the rank of matrix B = the result from step 1?
2
[{"matrix_cofactor": [[3, -6], [-6, 5]]}, {"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the matrix of cofactors for A = [[11, 4, 9], [-11, 12, 7], [12, 5, 11]]? Step 2: find rank(B) for B = the result from step 1.
3
[{"matrix_cofactor": [[97, 205, -199], [1, 13, -7], [-80, -176, 176]]}, {"matrix_rank": 3}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
For A = [[3, 2], [3, -4]], compute det(A).
-18.0
[{"determinant": -18.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
What is the transpose of A = [[-330, 498, 369], [139, 167, -618], [541, 498, 371]]?
[[-330, 139, 541], [498, 167, 498], [369, -618, 371]]
[{"matrix_transpose": [[-330, 139, 541], [498, 167, 498], [369, -618, 371]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
For A = [[2, -3], [2, -4]], compute det(A).
-2.0
[{"determinant": -2.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Given matrix A = [[53, -62, -119], [-16, 11, -132], [-164, -74, 172]], find ||A||_F.
317.13
[{"frobenius_norm": 317.13}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix for A = [[278, -156], [-61, -107]]. Step 2: evaluate the transpose of matrix B = the result from step 1. Step 3: what is the trace of C = the result from step 2?
171.0
[{"matrix_cofactor": [[-107, 61], [156, 278]]}, {"matrix_transpose": [[-107, 156], [61, 278]]}, {"matrix_trace": 171.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Evaluate the cofactor matrix of A = [[-9, -14], [5, -12]].
[[-12, -5], [14, -9]]
[{"matrix_cofactor": [[-12, -5], [14, -9]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find A^T for A = [[4, -2, -2], [4, -4, 3], [-2, 4, -4]]. Step 2: given matrix B = the result from step 1, find det(B).
-20.0
[{"matrix_transpose": [[4, 4, -2], [-2, -4, 4], [-2, 3, -4]]}, {"determinant": -20.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find A^T for A = [[-294, -189, 177], [99, -243, -30], [17, -112, -248]]. Step 2: what is ||B||_F for B = the result from step 1?
545.5
[{"matrix_transpose": [[-294, 99, 17], [-189, -243, -112], [177, -30, -248]]}, {"frobenius_norm": 545.5}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find the cofactor matrix for A = [[210, 314], [208, -214]]. Step 2: determine the transpose of matrix B = the result from step 1. Step 3: what is the trace of C = the result from step 2?
-4.0
[{"matrix_cofactor": [[-214, -208], [-314, 210]]}, {"matrix_transpose": [[-214, -314], [-208, 210]]}, {"matrix_trace": -4.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Given matrix A = [[2, -4, -3], [-3, -2, 4], [-3, 3, 2]], find det(A).
37.0
[{"determinant": 37.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: calculate the transpose of matrix A = [[-177, -169, -130], [53, 59, 154], [177, 86, 30]]. Step 2: calculate the Frobenius norm of matrix B = the result from step 1.
382.65
[{"matrix_transpose": [[-177, 53, 177], [-169, 59, 86], [-130, 154, 30]]}, {"frobenius_norm": 382.65}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the matrix of cofactors for A = [[-146, -279], [218, -227]]? Step 2: evaluate the transpose of matrix B = the result from step 1. Step 3: find tr(C) for C = the result from step 2.
-373.0
[{"matrix_cofactor": [[-227, -218], [279, -146]]}, {"matrix_transpose": [[-227, 279], [-218, -146]]}, {"matrix_trace": -373.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: compute the transpose of matrix A = [[-2, 3], [-3, -4]]. Step 2: for B = the result from step 1, compute det(B).
17.0
[{"matrix_transpose": [[-2, -3], [3, -4]]}, {"determinant": 17.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: find A^T for A = [[-151, -282], [169, -135]]. Step 2: find the Frobenius norm of matrix B = the result from step 1.
386.15
[{"matrix_transpose": [[-151, 169], [-282, -135]]}, {"frobenius_norm": 386.15}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: evaluate the transpose of matrix A = [[-227, -6], [129, -88]]. Step 2: what is ||B||_F for B = the result from step 1?
275.59
[{"matrix_transpose": [[-227, 129], [-6, -88]]}, {"frobenius_norm": 275.59}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: evaluate the transpose of matrix A = [[-25, -285], [135, -284]]. Step 2: what is the matrix of cofactors for B = the result from step 1? Step 3: what is the rank of matrix C = the result from step 2?
2
[{"matrix_transpose": [[-25, 135], [-285, -284]]}, {"matrix_cofactor": [[-284, 285], [-135, -25]]}, {"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Determine the transpose of matrix A = [[470, -483, 433], [-376, -333, 256], [-266, -408, -492]].
[[470, -376, -266], [-483, -333, -408], [433, 256, -492]]
[{"matrix_transpose": [[470, -376, -266], [-483, -333, -408], [433, 256, -492]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
What is the trace of A = [[-24, -3], [-51, 3]]?
-21.0
[{"matrix_trace": -21.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Find the cofactor matrix for A = [[4, 14], [-11, 12]].
[[12, 11], [-14, 4]]
[{"matrix_cofactor": [[12, 11], [-14, 4]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Find tr(A) for A = [[-42, -3, -6], [-42, -19, 12], [-37, 26, 19]].
-42.0
[{"matrix_trace": -42.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
What is the matrix of cofactors for A = [[13, 17], [-13, -9]]?
[[-9, 13], [-17, 13]]
[{"matrix_cofactor": [[-9, 13], [-17, 13]]}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: evaluate the cofactor matrix of A = [[5, -13], [-9, -3]]. Step 2: calculate the trace of matrix B = the result from step 1.
2.0
[{"matrix_cofactor": [[-3, 9], [13, 5]]}, {"matrix_trace": 2.0}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Given matrix A = [[26, 51, -137], [105, -84, 77], [8, -26, -88]], find ||A||_F.
233.54
[{"frobenius_norm": 233.54}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: calculate the transpose of matrix A = [[-451, -447], [-500, -391]]. Step 2: what is the matrix of cofactors for B = the result from step 1? Step 3: what is the rank of matrix C = the result from step 2?
2
[{"matrix_transpose": [[-451, -500], [-447, -391]]}, {"matrix_cofactor": [[-391, 447], [500, -451]]}, {"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: compute the transpose of matrix A = [[384, 11], [-144, -254]]. Step 2: what is the matrix of cofactors for B = the result from step 1? Step 3: determine the Frobenius norm of matrix C = the result from step 2.
482.52
[{"matrix_transpose": [[384, -144], [11, -254]]}, {"matrix_cofactor": [[-254, -11], [144, 384]]}, {"frobenius_norm": 482.52}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Find the rank of matrix A = [[13, 52], [-11, -78]].
2
[{"matrix_rank": 2}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: compute the transpose of matrix A = [[-145, -273], [-170, -222]]. Step 2: find the Frobenius norm of matrix B = the result from step 1.
416.82
[{"matrix_transpose": [[-145, -170], [-273, -222]]}, {"frobenius_norm": 416.82}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...
Step 1: what is the transpose of A = [[100, 90], [86, -11]]? Step 2: evaluate the Frobenius norm of matrix B = the result from step 1.
160.05
[{"matrix_transpose": [[100, 86], [90, -11]]}, {"frobenius_norm": 160.05}]
[ { "function": { "description": "Return the transpose of a matrix.", "name": "matrix_transpose", "parameters": { "properties": { "matrix": { "description": "Matrix represented as a list of rows (list[list[float | int]]).", "items": { "item...