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Exercise 6.2.4

Avg difficulty 3.0

Suppose TT is a linear transformation such that

T[11−8] = [131],T[−106] = [241],andT[0−13] = [61−1].T\left[\begin{array}{r}1\\ 1\\ -8\end{array}\right]~{}=~{}\left[\begin{array}{r}1\\ 3\\ 1\end{array}\right],\quad T\left[\begin{array}{r}-1\\ 0\\ 6\end{array}\right]~{}=~{}\left[\begin{array}{r}2\\ 4\\ 1\end{array}\right],\quad\text{and}\quad T\left[\begin{array}{r}0\\ -1\\ 3\end{array}\right]~{}=~{}\left[\begin{array}{r}6\\ 1\\ -1\end{array}\right].

Find the matrix of TT. Hint: use Exercise 7.

Selinger, Matrix Theory and Linear Algebra, Linear transformations in Rn, The matrix of a linear transformation, Exercise 6.2.4

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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.