+68 Let the vectors i and j be defined as usual:
\[\mathbf{i} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \mathbf{j} = \begin{pmatrix} 0 \\ 1 \end{pmatrix}.\]
Let A be a matrix such that Ai, Aj match the picture below:
Then for the vectors w,x,y and z above, calculate
\[\mathbf{A}^{-1} \mathbf{w}, \mathbf{A}^{-1} \mathbf{x}, \mathbf{A}^{-1} \mathbf{y}, \mathbf{A}^{-1} \mathbf{z}\]
and enter them in the order above. (Your answers should be numerical).
+228 Here are the answers:
\[\mathbf{A}^{-1} \mathbf{w} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\]
\[\mathbf{A}^{-1} \mathbf{x} = \begin{pmatrix} 4 \\ 0 \end{pmatrix}\]
\[\mathbf{A}^{-1} \mathbf{y} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}\]
\[\mathbf{A}^{-1} \mathbf{z} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}\]
