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Exercise 4.7.2

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. −3AT-3A{{}^{T}}.

  2. 3B−AT3B-A^{T}.

  3. ETBE^{T}B.

  4. EETEE^{T}.

  5. BTBB^{T}B.

  6. CATCA^{T}.

  7. DTBED^{T}BE.

Selinger, Matrix Theory and Linear Algebra, Matrices, The transpose, Exercise 4.7.2

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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.