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Exercise 6.2.3

Avg difficulty 3.0

Suppose TT is a linear transformation such that

T[12−6] = [513],T[−1−15] = [115],andT[0−12] = [53−2].T\left[\begin{array}{r}1\\ 2\\ -6\end{array}\right]~{}=~{}\left[\begin{array}{r}5\\ 1\\ 3\end{array}\right],\quad T\left[\begin{array}{r}-1\\ -1\\ 5\end{array}\right]~{}=~{}\left[\begin{array}{r}1\\ 1\\ 5\end{array}\right],\quad\text{and}\quad T\left[\begin{array}{r}0\\ -1\\ 2\end{array}\right]~{}=~{}\left[\begin{array}{r}5\\ 3\\ -2\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 6.2.3

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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.