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... |
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