Exercise · ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-003 · ★☆☆ Basic
The matrix of \(T\) is \(A=\begin{pmatrix}1&2\\0&3\end{pmatrix}\). What is \(T(2,-1)\)?
Choose one option.
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- B. \((0,\,-3)\)
Explanation
Multiply \(A\) by the column vector: \((1\cdot2+2\cdot(-1),\;0\cdot2+3\cdot(-1))=(0,-3)\).
Review the concept: Matrix of a linear transformation
The matrix \([T]\) of a linear transformation \(T\), with respect to given bases, has as columns the images of the domain basis vectors, written in coordinates of the codomain basis.
\[[T(v)]=[T]\,[v]\]
More practice problems: matrix of a linear transformation
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