1. What is a Matrices Calculator for Solving Systems?

Definition: This calculator solves for variable z in matrix equations of the form A x = b.

Purpose: It helps students and professionals solve systems of linear equations represented in matrix form.

2. How Does the Calculator Work?

The calculator solves the matrix equation:

Where:

• \( A \) — Coefficient matrix
• \( \mathbf{x} \) — Variable vector (including z)
• \( \mathbf{b} \) — Constant terms vector

Explanation: The system is solved using matrix operations to find the values of all variables.

3. Importance of Matrix Solutions

Details: Solving matrix equations is fundamental in engineering, physics, computer graphics, and many scientific applications.

4. Using the Calculator

Tips: Enter matrix A with rows separated by semicolons and columns by commas. Enter vector b as comma-separated values.

5. Frequently Asked Questions (FAQ)

Q1: What format should I use for the matrix?
A: Use semicolons between rows and commas between columns. Example: "1,2,3;4,5,6;7,8,9"

Q2: How do I specify which variable is z?
A: The calculator assumes the last variable in the system is z. Order your equations accordingly.

Q3: What methods are used to solve the system?
A: The calculator may use Gaussian elimination, LU decomposition, or other numerical methods.

Q4: Can I solve non-square systems?
A: The calculator handles square systems (n equations, n variables) and some over/under-determined cases.

Q5: What if my system has no solution?
A: The calculator will indicate if the system is inconsistent or has infinite solutions.