Find the matrix of the linear transformation with respect to the ordered basis{(0, −1), (−1, 0)}.
We are given a linear transformation $$ T : \mathbb{R}^2 \rightarrow \mathbb{R}^2 \text{ defined by } T(x, y) = (2y, x - y) $$ and we are to find the matrix of $T$ with respect to the ordered basis $$ B = \{ \mathbf{v}_1 = (0, -1),\ \mathbf{v}_2 = (-1, 0) \}. $$ --- ### Step 1: Apply $T$ to each basis vector #### _________ ____ ___ _________ _____ ______ ___ _________.
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Check whether the set of vectors is a linearly independent set of
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