(Step-by-Step) Let


Question: Let

\[M=\left[\begin{array}{cc} 1 & -1 \\ 1 & 1 \end{array}\right]\]

be the matrix of a linear transformation with respect to the standard basis. Let

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

be a basis of \(\mathbb{R}^{2}\). What is the matrix \([M]_{B}\) of the linear transformation of \(M\) with respect to the basis \(B\).

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