Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the identity matrix and O is the zero matrix. Show that A is invertible.
Suppose that A is an n × n matrix satisfying the equation A4 + 2A2 − 3A − I = O , where I is the identity matrix and O is the zero matrix. Show that A is invertible.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
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Suppose that A is an n × n matrix satisfying the equation
A4 + 2A2 − 3A − I = O ,
where I is the identity matrix and O is the zero matrix. Show that A is invertible.
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