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# How to solve Let $\mathbf{A}$ be an invertible matrix such that \[\mathbf{A} \begin{pmatrix} 1 \\ 2 \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \

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Let A be an invertible matrix such that $$\mathbf{A} \begin{pmatrix} 1 \\ 2 \end{pmatrix} = \begin{pmatrix} 1 \\ 1 \end{pmatrix}$$

and calculate $$\mathbf{A}^{-1} \begin{pmatrix} 2 \\ 2 \end{pmatrix}$$  if this expression is uniquely determined and defined.

Feb 26, 2019

$$A \begin{pmatrix}1\\ 2 \end{pmatrix} = \begin{pmatrix} 1 \\ 1\end{pmatrix}\\ 2A\begin{pmatrix}1\\ 2 \end{pmatrix} = \begin{pmatrix} 2 \\ 2\end{pmatrix}\\ A^{-1} \begin{pmatrix} 2 \\ 2\end{pmatrix} = 2 A^{-1}A\begin{pmatrix}1\\ 2 \end{pmatrix} =\begin{pmatrix}2\\4\end{pmatrix}$$