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Exercise 7.6.2

Avg difficulty 3.0

For each of the following matrices, determine whether it is invertible by checking whether the determinant is non-zero. If the determinant is non-zero, use the adjugate formula to find the inverse.

A=[123021310],B=[120021311],C=[133241011],D=[123021267],E=[103101310].A=\left[\begin{array}{rrr}1&2&3\\ 0&2&1\\ 3&1&0\\ \end{array}\right],\quad B=\left[\begin{array}{rrr}1&2&0\\ 0&2&1\\ 3&1&1\\ \end{array}\right],\quad C=\left[\begin{array}{rrr}1&3&3\\ 2&4&1\\ 0&1&1\\ \end{array}\right],\quad D=\left[\begin{array}{rrr}1&2&3\\ 0&2&1\\ 2&6&7\\ \end{array}\right],\quad E=\left[\begin{array}{rrr}1&0&3\\ 1&0&1\\ 3&1&0\\ \end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Determinants, Application: A formula for the inverse of a matrix, Exercise 7.6.2

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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.