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Exercise 10.4.8

Avg difficulty 3.0

Let v=[1−23]\mathbf{v}=\left[\begin{array}{r}1\\ -2\\ 3\end{array}\right] and consider the linear function T(w)=proj⁡v(w)T(\mathbf{w})=\operatorname{proj}_{\mathbf{v}}(\mathbf{w}). Find the matrix of TT with respect to the basis

B={v1,v2,v3}={[1−23], [210], [301]}.B=\left\{\mathbf{v}_{1},\mathbf{v}_{2},\mathbf{v}_{3}\right\}=\left\{\left[\begin{array}{r}1\\ -2\\ 3\end{array}\right],~{}\left[\begin{array}{r}2\\ 1\\ 0\end{array}\right],~{}\left[\begin{array}{r}3\\ 0\\ 1\end{array}\right]\right\}.

Selinger, Matrix Theory and Linear Algebra, Linear transformation of vector spaces, The matrix of a linear transformation, Exercise 10.4.8

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.