11TH•Mathematics•Matrices And Determinants•4.8 Non-Homogeneous Systems

4.8 System of Non-Homogeneous Linear Equations

Consistent and inconsistent systems via reduced echelon, matrix inversion, and Cramer's rule.

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A system

\begin{align*} a_1 x + b_1 y + c_1 z &= d_1 \\ a_2 x + b_2 y + c_2 z &= d_2 \\ a_3 x + b_3 y + c_3 z &= d_3 \end{align*}

is non-homogeneous if not all of $d_1, d_2, d_3$ are zero.

Methods: reduced echelon form, matrix inversion, Cramer's rule.

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