# System of Equations: Solve using Inverse of Coefficient Matrix

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Solve the following system of equations by computing the inverse of the coefficient matrix.

-x+2y =4

2x-y+2z = -2

2y-z = 4

https://brainmass.com/math/matrices/system-equations-solve-inverse-coefficient-matrix-12662

#### Solution Preview

Three equations can be re written as:

-x + 2y + 0.z = 4 ....(1)

2x - y + 2z = -2 ....(2)

0.x + 2y - z = 4 ....(3)

The equation can be written in the form of three matrices A, X, and B as:

AX = B

Matrix A:

a11 = -1, a12 = 2, a13 = 0

a21 = 2, a22 = -1, a23 = 2

a31 = 0, a32 = 2, a33 = ...

#### Solution Summary

A system of equations is solved by computing the inverse of the coefficient matrix.

$2.49