Question 5 Let n be a positive integer and J the n × n matrix for which every entry is 1. Verify that I - J is invertible if and only if n ≥ 2, in which case (I – J)−¹ = 1 I n J. 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 14E
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Question 5
Let n be a positive integer and J the n × n matrix for which every entry is 1. Verify that I - J is
invertible if and only if n ≥ 2, in which case
(I – J)−¹
=
1
I
n
J.
1
Transcribed Image Text:Question 5 Let n be a positive integer and J the n × n matrix for which every entry is 1. Verify that I - J is invertible if and only if n ≥ 2, in which case (I – J)−¹ = 1 I n J. 1
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