Base change/Transformation matrix/Standard basis and 451/23-8/57-3/Exercise

Determine the transformation matrices ${}M_{\mathfrak {v}}^{\mathfrak {u}}$ and ${}M_{\mathfrak {u}}^{\mathfrak {v}}$ for the standard basis ${}{\mathfrak {u}}$ and the basis ${}{\mathfrak {v}}$ of ${}\mathbb {R} ^{3}$ that is given by the vectors

$v_{1}={\begin{pmatrix}4\\5\\1\end{pmatrix}},\,\,v_{2}={\begin{pmatrix}2\\3\\-8\end{pmatrix}},\,{\text{ and }}\,v_{3}={\begin{pmatrix}5\\7\\-3\end{pmatrix}}$

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