Answer
The inverse of the given matrix is:
\[ \left( \begin{array}{ccc}
1 & 1\\
0 & 1 \end{array} \right)\]
Work Step by Step
1. Put an identity $I$ matrix on the right of the given matrix, to get a $2 \times 4$ one.
\[ \left( \begin{array}{ccc}
1 & -1 & 1 & 0\\
0 & 1 & 0 & 1 \end{array} \right)\]
2. Row-reduce the whole matrix:
- $a_{12}$ must be equal to 0. In order to get there, we can do this operation:
$R_1 = R_1 + R_2$:
$a_{11} = a_{11} + a_{21} = 1 + 0 = 1$
$a_{12} = a_{12} + a_{22} = -1 + 1 = 0$
$a_{13} = a_{13} + a_{23} = 1 + 0 = 1$
$a_{14} = a_{14} + a_{24} = 0 + 1 = 1$
\[ \left( \begin{array}{ccc}
1 & 0 & 1 & 1\\
0 & 1 & 0 & 1 \end{array} \right)\]
- The inverse of the given matrix is:
\[ \left( \begin{array}{ccc}
1 & 1\\
0 & 1 \end{array} \right)\]
