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Exercise 6.4.7

Avg difficulty 3.0

Let TT be the linear transformation with matrix A=[31−12]A=\left[\begin{array}{rr}3&1\\ -1&2\end{array}\right] and SS the linear transformation with matrix B=[0−242]B=\left[\begin{array}{rr}0&-2\\ 4&2\end{array}\right]. Find the matrix of S∘TS\circ T. Compute (S∘T)(v)(S\circ T)(\mathbf{v}) for v=[2−1]\mathbf{v}=\left[\begin{array}{r}2\\ -1\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Linear transformations in Rn, Properties of linear transformations, Exercise 6.4.7

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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.