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Exercise 4.5.4

Avg difficulty 3.0

For each of the following matrices, find the inverse if possible. If the inverse does not exist, explain why.

A=[21−13],B=[0153],C=[2130],D=[2142],E=[012125].A=\left[\begin{array}{rr}2&1\\ -1&3\end{array}\right],\quad B=\left[\begin{array}{rr}0&1\\ 5&3\end{array}\right],\quad C=\left[\begin{array}{rr}2&1\\ 3&0\end{array}\right],\quad D=\left[\begin{array}{rr}2&1\\ 4&2\end{array}\right],\quad E=\left[\begin{array}{rrr}0&1&2\\ 1&2&5\\ \end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Matrices, Matrix inverses, Exercise 4.5.4

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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.