Exercise · ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-004 · ★☆☆ Basic
It is known that \(T(e_1)=(1,4)\) and \(T(e_2)=(-2,5)\). What is the matrix of \(T\) in the standard bases?
Choose one option.
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- D. \(\begin{pmatrix}1&-2\\4&5\end{pmatrix}\)
Explanation
The images of the basis vectors are the columns: the first column is \((1,4)\) and the second \((-2,5)\). Writing them as rows gives the transpose, a different matrix.
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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