Exact matrix calculations with step-by-step results for six core matrix operations.
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Add two matrices of the same dimensions entry by entry. Useful for exact matrix addition or explaining each entry step by step. Accepts integers, decimals, and fraction strings (for example 1/2); returns the exact sum matrix and a calculation for each position.
First matrix.
Second matrix.
Add two matrices of the same dimensions entry by entry. Useful for exact matrix addition or explaining each entry step by step. Accepts integers, decimals, and fraction strings (for example 1/2); returns the exact sum matrix and a calculation for each position.
| Argument | Type | Description |
|---|---|---|
| matrixA* | array | First matrix. |
| matrixB* | array | Second matrix. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"matrixA",
"matrixB"
],
"properties": {
"matrixA": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "First matrix."
},
"matrixB": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Second matrix."
}
}
}Find the exact determinant of a square matrix using fraction-preserving elimination. Use for determinant questions requiring row swaps, elimination steps, pivot multipliers, sign changes, diagonal products, or singularity checks. Returns the determinant and detailed operation steps.
| Argument | Type | Description |
|---|---|---|
| matrix* | array | Square matrix. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"matrix"
],
"properties": {
"matrix": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Square matrix."
}
}
}Find an exact inverse of a square matrix with step-by-step Gauss-Jordan elimination. Use for inverse questions needing exact fractions, augmented matrices, row swaps, normalization, elimination, and verification that A times A-inverse is identity. Returns the inverse and verification, or null with singular=true if not invertible.
| Argument | Type | Description |
|---|---|---|
| matrix* | array | Square matrix. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"matrix"
],
"properties": {
"matrix": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Square matrix."
}
}
}Multiply A by B when A's column count equals B's row count, including non-square matrices. Useful for exact matrix multiplication and step-by-step row-by-column dot products. Returns exact results plus each factor pair, product, and entry calculation; accepts fractions and decimals.
| Argument | Type | Description |
|---|---|---|
| matrixA* | array | Left matrix A. |
| matrixB* | array | Right matrix B. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"matrixA",
"matrixB"
],
"properties": {
"matrixA": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Left matrix A."
},
"matrixB": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Right matrix B."
}
}
}Subtract matrix B from matrix A when both have the same dimensions. Useful for exact matrix subtraction, including negative values and step-by-step entry calculations. Accepts integers, decimals, and fraction strings; returns each exact difference and its calculation.
| Argument | Type | Description |
|---|---|---|
| matrixA* | array | Matrix to subtract from. |
| matrixB* | array | Matrix to subtract. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"matrixA",
"matrixB"
],
"properties": {
"matrixA": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Matrix to subtract from."
},
"matrixB": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Matrix to subtract."
}
}
}Transpose a rectangular or square matrix by exchanging rows and columns. Useful for requests to show where each result entry originated. Preserves exact integer, decimal, and fraction inputs and returns the transposed matrix with source-to-result position mappings.
| Argument | Type | Description |
|---|---|---|
| matrix* | array | Matrix to transpose. |
{
"type": "object",
"$schema": "https://json-schema.org/draft/2020-12/schema",
"required": [
"matrix"
],
"properties": {
"matrix": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": [
"string",
"number"
]
},
"minItems": 1
},
"minItems": 1,
"description": "Matrix to transpose."
}
}
}