Chapter 10 - Chapter Test - Page 764: 2

$\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &0 & 0 & 0 \\ 0 & 0& 0 & 0 \end{bmatrix}$

Work Step by Step

We will add $R_1$ to $R_2$, subtract $R_1$ from row $3$ and subtract $3R_1$ from $R_4$. We have: $\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &1 & 0 & -1 \\ 0 & 2& 0 & -2 \end{bmatrix}$ Now, we subtract $R_2$ from $R_3$ and $2 R_2$ from $R_4$. We have: $\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &0 & 0 & 0 \\ 0 & 0& 0 & 0 \end{bmatrix}$ Finally, we have: $\begin{bmatrix} 1 &0 & -1 & 2 \\ 0 & 1 & 0 &-1 \\ 0 &0 & 0 & 0 \\ 0 & 0& 0 & 0 \end{bmatrix}$

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