College Algebra, Chapter 7, 7.3, Section 7.3, Problem 30

Solve the system of equations $\left\{
\begin{equation}
\begin{aligned}

5x + 7y + 4z =& 1
\\
3x - y + 3z =& 1
\\
6x + 7y + 5z =& 1

\end{aligned}
\end{equation}
\right.
$, $\displaystyle \left[ \begin{array}{ccc}
26 & 7 & -25 \\
-3 & -1 & 3 \\
-27 & -7 & 26
\end{array} \right] $ by converting to a matrix equation and using the inverse of the coefficient matrix $\left[ \begin{array}{cc}
-9 & 4 \\
7 & -3
\end{array} \right]$

The equivalent matrix equation is







Using the formula for solving a matrix equation

$X = A^{-1} B$

We have







Thus, $x = 8, y = -1$ and $z = -8$ is the solution of the original system.