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Exercise 6.1.1

Avg difficulty 3.0

Which of the following vector functions are linear transformations?

T1([xy])=[2x+yx−2y−x−y],T2([xyz])=[x+y2(x+y)z0],T3([xyz])=[00].T_{1}\left(\left[\begin{array}{c}x\\ y\end{array}\right]\right)=\left[\begin{array}{c}2x+y\\ x-2y\\ -x-y\end{array}\right],\quad T_{2}\left(\left[\begin{array}{c}x\\ y\\ z\end{array}\right]\right)=\left[\begin{array}{c}x+y^{2}\\ (x+y)z\\ 0\end{array}\right],\quad T_{3}\left(\left[\begin{array}{c}x\\ y\\ z\end{array}\right]\right)=\left[\begin{array}{c}0\\ 0\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Linear transformations in Rn, Linear transformations, Exercise 6.1.1

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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.