## Precalculus (6th Edition) Blitzer

The new matrix, $\left[ \begin{matrix} 1 & 2 & 2 & 2 \\ 0 & 1 & -1 & 2 \\ 0 & 0 & 9 & -9 \\ \end{matrix} \right]$
Consider the given matrix, $\left[ \begin{matrix} 1 & 2 & 2 & 2 \\ 0 & 1 & -1 & 2 \\ 0 & 5 & 4 & 1 \\ \end{matrix} \right]$ Perform the operation, $-5{{R}_{2}}+{{R}_{3}}$ For this we will first multiply row 2 by $\left( -5 \right)$ to get, \begin{align} & 0\left( -5 \right)=0 \\ & 1\left( -5 \right)=-5 \\ & -1\left( -5 \right)=5 \\ & 2\left( -5 \right)=-10 \end{align} Now adding this with row 3 as below, we get: $\left[ \begin{matrix} 1 & 2 & 2 & 2 \\ 0 & 1 & -1 & 2 \\ 0+0 & 5+\left( -5 \right) & 4+5 & 1+\left( -10 \right) \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 2 & 2 & 2 \\ 0 & 1 & -1 & 2 \\ 0 & 0 & 9 & -9 \\ \end{matrix} \right]$ The new matrix is: $\left[ \begin{matrix} 1 & 2 & 2 & 2 \\ 0 & 1 & -1 & 2 \\ 0 & 0 & 9 & -9 \\ \end{matrix} \right]$