1. What is a System Of Linear Equations?

A system of linear equations is a collection of one or more linear equations involving the same set of variables. The solution to the system is the set of values that satisfies all equations simultaneously.

2. How Does the Calculator Work?

The calculator solves the matrix equation:

Where:

• \( A \) — Coefficient matrix
• \( x \) — Unknown variable vector
• \( B \) — Constant vector

Method: The calculator computes the solution using \( x = A^{-1} B \), where \( A^{-1} \) is the inverse of matrix A.

3. Importance of Solving Linear Systems

Details: Solving systems of linear equations is fundamental in various fields including engineering, physics, economics, and computer science. It's used for circuit analysis, structural analysis, optimization problems, and many other applications.

4. Using the Calculator

Tips: Enter matrix A as comma-separated rows with semicolons separating different rows. Enter vector B as comma-separated values. The matrix must be square and non-singular (invertible).

5. Frequently Asked Questions (FAQ)

Q1: What if the matrix is not invertible?
A: If the matrix is singular (determinant = 0), the system may have no solution or infinitely many solutions. The calculator will indicate if the matrix is singular.

Q2: What are the limitations of this method?
A: Matrix inversion can be numerically unstable for ill-conditioned matrices. For large systems, other methods like Gaussian elimination or iterative methods may be more appropriate.

Q3: Can I solve non-square systems?
A: This calculator only solves square systems (number of equations = number of unknowns). For non-square systems, least squares solutions may be needed.

Q4: What precision does the calculator use?
A: The calculator uses double precision floating point arithmetic with results rounded to 4 decimal places for display.

Q5: Are there alternative methods to solve linear systems?
A: Yes, other methods include Gaussian elimination, LU decomposition, Cholesky decomposition, and iterative methods like Jacobi or Gauss-Seidel.