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Exercise 4.5.5

Avg difficulty 3.0

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

A=[123214102],B=[103234102],C=[1232144510],D=[1202112021−321212].A=\left[\begin{array}{rrr}1&2&3\\ 2&1&4\\ 1&0&2\end{array}\right],\quad B=\left[\begin{array}{rrr}1&0&3\\ 2&3&4\\ 1&0&2\end{array}\right],\quad C=\left[\begin{array}{rrr}1&2&3\\ 2&1&4\\ 4&5&10\end{array}\right],\quad D=\left[\begin{array}{rrrr}1&2&0&2\\ 1&1&2&0\\ 2&1&-3&2\\ 1&2&1&2\end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Matrices, Matrix inverses, Exercise 4.5.5

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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.