Exercise · ZW-MATRIX-OF-A-LINEAR-TRANSFORMATION-001 · ★☆☆ Basic
What is the matrix of \(T(x,y)=(2x+y,\,3x-y)\) in the standard bases?
Choose one option.
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- A. \(\begin{pmatrix}2&1\\3&-1\end{pmatrix}\)
Explanation
The coefficients of each component form a row: the first is \((2,1)\) and the second \((3,-1)\). This is the same as using \(T(e_1)=(2,3)\) and \(T(e_2)=(1,-1)\) as columns.
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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