Use Inverses to Solve Matrix Equations
Write the linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the
constant matrix.
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\begin{array} { l } 5 x + 2 y - 2 z = 37 \\4 x + 3 y + 5 z = 22 \\7 x - 2 y + 6 z = 15\end{array}

\left[ \begin{array} { r r r } 5 & 2 & - 2 \\4 & 3 & 5 \\7 & - 2 & 6\end{array} \right] \left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { l } 37 \\22 \\15\end{array} \right]

\left[ \begin{array} { c c r } 5 & 4 & 7 \\ 2 & 3 & - 2 \\ - 2 & 5 & 6 \end{array} \right] \left[ \begin{array} { l } x \\ y \\ z \end{array} \right] = \left[ \begin{array} { l } 37 \\ 22 \\ 15 \end{array} \right]

\left[ \begin{array} { r r r } 37 & - 2 & 2 \\22 & 5 & 3 \\15 & 6 & - 2\end{array} \right] \left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { l } 5 \\4 \\7\end{array} \right]

\left[ \begin{array} { l l } 5 & 2 \\4 & 3 \\7 & - 2\end{array} \right] \left[ \begin{array} { l } x \\y \\z\end{array} \right] = \left[ \begin{array} { l } - 2 \\5 \\6\end{array} \right]

Use Matrices and Gauss-Jordan Elimination to Solve Systems Solve the System

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Use Matrices and Gauss-Jordan Elimination to Solve Systems
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