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Exercise 4.4.6

Avg difficulty 3.0

Consider the matrices

A=[123217],B=[3−12−321],C=[1231],D=[−122−3],E=[23].A=\left[\begin{array}{rrr}1&2&3\\ 2&1&7\end{array}\right],\quad B=\left[\begin{array}{rrr}3&-1&2\\ -3&2&1\end{array}\right],\quad C=\left[\begin{array}{rr}1&2\\ 3&1\end{array}\right],\quad D=\left[\begin{array}{rr}-1&2\\ 2&-3\end{array}\right],\quad E=\left[\begin{array}{r}2\\ 3\end{array}\right].

Find the following if possible. If it is not possible explain why.

  1. −3A-3A

  2. 3B−A3B-A

  3. ACAC

  4. CBCB

  5. AEAE

  6. EAEA

Selinger, Matrix Theory and Linear Algebra, Matrices, Matrix multiplication, Exercise 4.4.6

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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.