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Exercise 7.6.3

Avg difficulty 3.0

Determine whether each of the following matrices is invertible. If so, use the adjugate formula to find the inverse. If the inverse does not exist, explain why.

A=[1112],B=[123021411],C=[121230012].A=\left[\begin{array}{rr}1&1\\ 1&2\\ \end{array}\right],\quad B=\left[\begin{array}{rrr}1&2&3\\ 0&2&1\\ 4&1&1\\ \end{array}\right],\quad C=\left[\begin{array}{rrr}1&2&1\\ 2&3&0\\ 0&1&2\\ \end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Determinants, Application: A formula for the inverse of a matrix, Exercise 7.6.3

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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.