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Exercise 4.4.7

Avg difficulty 3.0

Consider the matrices

A=[12321−1],B=[2−52−321],C=[1250],D=[−114−3],E=[13]A=\left[\begin{array}{rr}1&2\\ 3&2\\ 1&-1\end{array}\right],\quad B=\left[\begin{array}{rrr}2&-5&2\\ -3&2&1\end{array}\right],\quad C=\left[\begin{array}{rr}1&2\\ 5&0\end{array}\right],\quad D=\left[\begin{array}{rr}-1&1\\ 4&-3\end{array}\right],\quad E=\left[\begin{array}{r}1\\ 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. CACA

  5. AEAE

  6. EAEA

  7. BEBE

  8. DEDE

Selinger, Matrix Theory and Linear Algebra, Matrices, Matrix multiplication, Exercise 4.4.7

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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.