Linear System Solver
Solve Ax=b for square linear systems with matrix and vector input.
Formula / method
x = A⁻¹b when A is invertible; row-reduction concepts apply more generally.
How to use
Use the stated mathematical relationship and keep signs, units and order of operations consistent.
What this calculator answers
The Linear System Solver uses the requested values to calculate the requested result. The core method is x = A⁻¹b when A is invertible; row-reduction concepts apply more generally.. This makes the assumptions visible so you can check whether the inputs match your situation.
How to get a useful result
Use the stated mathematical relationship and keep signs, units and order of operations consistent.
How to interpret it
The result is a mathematical value based only on the numbers entered; check domain restrictions such as division by zero, roots and logarithms.
Before relying on the number
Recheck unusual inputs, confirm units and compare the result with any official quote, statement, specification or rule that applies to the real decision. Small changes in rates, time periods or measurements can materially change some results.