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Let A be a \(2 \times 2\) matrix. Suppose that for every two-dimensional vector v, there exists a two-dimensional vector w such that \(\mathbf{A} \mathbf{w} = \mathbf{v}\)
Show that we can find a matrix B such that \(\mathbf{A} \mathbf{B} = \mathbf{I}\).

 Mar 13, 2019
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\(\exists w_1 \ni A w_1 = \begin{pmatrix}1\\0\end{pmatrix}\\ \exists w_2 \ni A w_2 = \begin{pmatrix}0\\1\end{pmatrix}\\ B = \begin{pmatrix}w_1 &w_2\end{pmatrix}\)

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 Mar 13, 2019

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