[Solution] The vectors


Question: The vectors

\[B=\left(\left[\begin{array}{l} 2 \\ 3 \end{array}\right],\left[\begin{array}{l} 1 \\ 2 \end{array}\right]\right)\]

form a basis of \(\mathbb{R}^{2}\).

a: Find the coordinates with respect to the standard basis of the vector \(v\) whose coordinates with respect to \(B\) are

\[[v]_{B}=\left[\begin{array}{c} -2 \\ 1 \end{array}\right]\]

b: Find the coordinates with respect to the basis \(B\) of the vector with coordinates

\[\left[\begin{array}{c} -2 \\ 1 \end{array}\right]\]

in the standard basis.

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Solution: The downloadable solution consists of 2 pages
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