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Exercise 4.4.1

Avg difficulty 3.0

Let A=[120−111]A=\left[\begin{array}{rrr}1&2&0\\ -1&1&1\end{array}\right]. Multiply AA by each of the following vectors.

(a) [100],(b) [01−1],(c) [210],(d) [000],(e) [103].(a)~{}\left[\begin{array}{r}1\\ 0\\ 0\end{array}\right],\quad(b)~{}\left[\begin{array}{r}0\\ 1\\ -1\end{array}\right],\quad(c)~{}\left[\begin{array}{r}2\\ 1\\ 0\end{array}\right],\quad(d)~{}\left[\begin{array}{r}0\\ 0\\ 0\end{array}\right],\quad(e)~{}\left[\begin{array}{r}1\\ 0\\ 3\end{array}\right].\quad

Selinger, Matrix Theory and Linear Algebra, Matrices, Matrix multiplication, Exercise 4.4.1

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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.