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    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

    © BrainMass Inc. brainmass.com March 4, 2021, 5:49 pm ad1c9bdddf
    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

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