Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 726: 67

Part A: $\begin{bmatrix} 2 & 3\\ 1 & 4\\ \end{bmatrix}$$\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} 5\\ 10\\ \end{bmatrix}$ Part B: $\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} -2\\ 3\\ \end{bmatrix}$

Part A: $\begin{bmatrix} 2 & 3\\ 1 & 4\\ \end{bmatrix}$$\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} 5\\ 10\\ \end{bmatrix}$ Part B: Gauss Jordan Elimination: $\begin{bmatrix} 2 & 3 & |5\\ 1 & 4 & |10\\ \end{bmatrix}$ ~ $\begin{bmatrix} 2 & 3 & |5\\ 0 & -5 & |-15\\ \end{bmatrix}$ ~ $\begin{bmatrix} 2 & 3 & |5\\ 0 & 1 & |3\\ \end{bmatrix}$ ~ $\begin{bmatrix} 2 & 0 & |-4\\ 0 & 1 & |3\\ \end{bmatrix}$ ~ $\begin{bmatrix} 1 & 0 & |-2\\ 0 & 1 & |3\\ \end{bmatrix}$ Therefore the answer is: $\begin{bmatrix} x_{1}\\ x_{2}\\ \end{bmatrix}$ = $\begin{bmatrix} -2\\ 3\\ \end{bmatrix}$