1. What is the Matrix Equation Solver?

The matrix equation solver calculates the solution to the system of linear equations represented by AX = B, where A is a square coefficient matrix, X is the unknown vector, and B is the constant vector. The solution is found by computing X = A⁻¹B.

2. How Does the Calculator Work?

The calculator uses matrix inversion to solve the equation:

Where:

• \( A \) — Square coefficient matrix (n×n)
• \( B \) — Constant vector (n×1)
• \( X \) — Solution vector (n×1)

Explanation: The calculator first validates the matrix dimensions, then performs matrix inversion (when possible) followed by matrix multiplication.

3. Importance of Matrix Equations

Details: Matrix equations are fundamental in engineering, physics, computer graphics, and machine learning. They provide compact representations of systems of linear equations.

4. Using the Calculator

Tips: Enter the coefficient matrix A with one row per line, elements separated by spaces. Enter vector B as a column of values. The matrices must be square and properly dimensioned.

5. Frequently Asked Questions (FAQ)

Q1: What matrix sizes are supported?
A: The calculator supports small to medium matrices (typically up to 10×10 for practical computation).

Q2: What if my matrix is singular?
A: The calculator will return an error if the matrix is singular (non-invertible). Consider using least squares methods for such cases.

Q3: How precise are the results?
A: Results are limited by floating-point precision. For ill-conditioned matrices, results may have significant numerical errors.

Q4: Can I solve non-square systems?
A: This calculator only solves square systems. For rectangular matrices, different approaches like QR decomposition are needed.

Q5: What's the computational complexity?
A: Matrix inversion is O(n³) for an n×n matrix, so performance degrades with larger matrices.