Application: A formula for the inverse of a matrix
Checking invertibility via the determinant, then computing inverses with the adjugate formula built from cofactors.
Matrix Theory and Linear Algebra, Application: A formula for the inverse of a matrix
10 exercises
Exercise 7.6.2
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.
Exercise 7.6.3
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.
Exercise 7.6.4
Use the adjugate formula to find the inverse of the matrix
Exercise 7.6.5
Use the adjugate formula to find the inverse of the matrix
Exercise 7.6.6
Consider the matrix
Does there exist a value of for which this matrix fails to be invertible? Explain.
Exercise 7.6.7
Consider the matrix
Does there exist a value of for which this matrix fails to be invertible? Explain.
Exercise 7.6.8
Consider the matrix
Does there exist a value of for which this matrix fails to be invertible? Explain.
Exercise 7.6.9
Consider the matrix
Does there exist a value of for which this matrix fails to be invertible? Explain.
Exercise 7.6.10
Use the adjugate formula to find the inverse of the matrix
Exercise 7.6.11
Find the inverse, if it exists, of the matrix
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.