Maths Matrix Calculator

Matrix Operations:

\[ \text{det}(A), A^{-1}, A + B, A - B, A \times B \]

Operation:

Matrix A: Enter matrix as comma-separated rows, e.g., "1,2,3" for first row

Matrix B: Required for addition, subtraction, and multiplication

Result:

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1. What is Matrix Calculator?

The Matrix Calculator performs various operations on matrices including determinant calculation, matrix inversion, addition, subtraction, and multiplication. Matrices are fundamental in linear algebra and have applications in physics, engineering, and computer science.

2. How Does the Calculator Work?

The calculator performs the following operations:

\[ \begin{align*} \text{det}(A) &= \text{Determinant of matrix } A \\ A^{-1} &= \text{Inverse of matrix } A \\ A + B &= \text{Matrix addition} \\ A - B &= \text{Matrix subtraction} \\ A \times B &= \text{Matrix multiplication} \end{align*} \]

Requirements:

For addition/subtraction: Matrices must have same dimensions
For multiplication: Columns of A must equal rows of B
For inverse/determinant: Matrix must be square

3. Importance of Matrix Operations

Applications: Matrix operations are essential for solving systems of linear equations, computer graphics transformations, quantum mechanics, and machine learning algorithms.

4. Using the Calculator

Instructions:

Select the operation you want to perform
Enter matrix A in the text area (one row per line, comma-separated values)
For operations requiring two matrices, enter matrix B
Click Calculate to see the result

5. Frequently Asked Questions (FAQ)

Q1: What is the determinant used for?
A: The determinant can determine if a matrix is invertible, calculate the volume scaling factor of a linear transformation, and solve systems of linear equations.

Q2: Why can't some matrices be inverted?
A: A matrix is invertible only if its determinant is non-zero. Matrices with determinant zero are called singular.

Q3: Is matrix multiplication commutative?
A: No, matrix multiplication is not commutative (A×B ≠ B×A in general).

Q4: What's the difference between matrix and scalar operations?
A: Matrix operations follow specific rules of linear algebra, while scalar operations work element-wise.

Q5: Are there size limits for matrices?
A: The calculator can handle reasonable matrix sizes, but very large matrices may cause performance issues.