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Applied Mathematics · Ch 2 — Algebra

Inverse of Coefficient Matrix

2.8.1

Inverse of Coefficient Matrix

Once a system of equations is written in matrix form AX=BAX = B, and provided the coefficient matrix AA is invertible (that is, ∣A∣≠0|A| \neq 0), the solution can be found directly by multiplying both sides on the left by A−1A^{-1}:

AX=B  ⟹  X=A−1BAX = B \implies X = A^{-1}B …

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