How are matrices used to solve a system of several linear equations at once?
Write the system in the form AX = B, where A holds the coefficients, X the unknowns and B the constants.
Write the system in the form AX = B, where A holds the coefficients, X the unknowns and B the constants. If A is invertible (det A ≠ 0), multiply both sides on the left by A⁻¹ to get X = A⁻¹B — one clean formula that delivers all the unknowns together. This is far more systematic than elimination for large systems and is exactly how software solves engineering and economics models.
Key point
AX = B ⇒ X = A⁻¹B when det A ≠ 0.
Common mistake
writing X = B/A — matrices can't be divided.
Memory tip
package the system as AX = B, then hit it with A⁻¹.
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