Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 726: 68

Part A: $\begin{bmatrix} -2 & -3\\ 6 & 1\\ \end{bmatrix}$$\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} -4\\ -36\\ \end{bmatrix}$ Part B: $\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} -7\\ 6\\ \end{bmatrix}$

Part A: $\begin{bmatrix} -2 & -3\\ 6 & 1\\ \end{bmatrix}$$\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} -4\\ -36\\ \end{bmatrix}$ Part B: Gauss Jordan Elimination: $\begin{bmatrix} -2 & -3 & |-4\\ 6 & 1 & |-36\\ \end{bmatrix}$ ~ $\begin{bmatrix} -2 & -3 & |-4\\ 0 & -8 & |-48\\ \end{bmatrix}$ ~ $\begin{bmatrix} -2 & -3 & |-4\\ 0 & 1 & |6\\ \end{bmatrix}$ ~ $\begin{bmatrix} -2 & 0 & |14\\ 0 & 1 & |6\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & |-7\\ 0 & 1 & |6\\ \end{bmatrix}$ Therefore the answer is: $\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} -7\\ 6\\ \end{bmatrix}$