Find the standard matrix of the linear transformation of $T(x,y,3)=(x-y,3-2x)$.
I'm thinking it's $$\begin{bmatrix}1&-1\\3-2x&0\end{bmatrix}$$ but I'm not too sure.
2026-04-02 18:43:01.1775155381
Find the standard matrix of the linear transformation of $T(x,y,3)=(x-y,3-2x)$
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Remember that transformation matrices cannot use any of the variables provided to them as input. The 3 is in the input to allow you to put the 3 into $3-2x$ and we are mapping from $\mathbb R^3\to\mathbb R^2$, so we must have this 2×3 transformation matrix as the answer. $$\begin{bmatrix} 1&-1&0\\ -2&0&1\end{bmatrix}$$