Can Matrix Calculator (matrixcalc.org) Solve Systems of Linear Equations?

Updated

Yes. Matrix Calculator at matrixcalc.org can solve systems of linear equations written in the matrix form A*X=B. You enter the coefficient matrix A and the constant matrix B, and the site returns the solution along with the solution steps. It also handles related equation forms such as Y+A=B. The tool works on non-square matrices too, as long as you leave the extra cells empty.

How the A*X=B solver works

A system of linear equations can be written compactly as A*X=B, where:

  • A is the coefficient matrix (one row per equation, one column per variable)
  • X is the column vector of unknowns you want to find
  • B is the constant matrix (the right-hand side values)

The calculator solves for X. Because the site also computes the inverse matrix and other operations, it can approach the system through matrix methods rather than only substitution.

Steps to solve a system

  1. Open matrixcalc.org.
  2. Enter the coefficients into Matrix A. For example, a 3-equation, 3-variable system uses a 3×3 matrix.
  3. Enter the constants into Matrix B as a column.
  4. Select the A*X=B option (the solver mode shown in the interface).
  5. Run the calculation and read the solution, which is displayed together with the solution steps.

Example input format: the site accepts matrix literals such as {{1,2,3},{4,5,6},{7,2,9}}, so you can type a matrix directly instead of filling cells one by one.

What you can expect as output

  • The solution vector X for the system.
  • Solution steps, so you can follow how the result was reached.
  • Support for multiple equations, since the matrices can be larger than 2×2.

Related equation forms

The interface also lists Y+A=B alongside A*X=B. This lets you solve matrix equations where the unknown matrix appears in an addition relationship, not only in a product.

Practical notes

  • You can enter decimal fractions or mathematical expressions (for example 1/3, 2^0.5, sin(phi)), which is useful when coefficients are not whole numbers.
  • Non-square matrices are allowed — leave extra cells empty.
  • Navigation and editing use standard keys: Enter, Space, arrow keys, Backspace, and Delete; copy and paste with Ctrl/Cmd + C and Ctrl/Cmd + V.
  • Results can be dragged and dropped from the results area, or to and from a text editor.

If your goal is simply to get the unknown values for a linear system, entering A and B and using the A*X=B solver is the direct path. If you also want to inspect the underlying structure, the same site offers determinant, inverse, rank, and decomposition tools that complement the solve.