Nilpotent matrix Give a 3 by 3 matrix A such that AA#0, A² 0, and A³ = 0. Inverse and pseudo-inverse 1. Given that the inverse of AT A exists, show that A has a left pseudoinverse-that is, there exists a matrix B such that BA = I. 2. Given that the inverse of AA exists, show that A has a right pseudoinverse-that is, there exists a matrix C such that AC = I. 3. Show that if BA = I and AC = I then B = C.
Nilpotent matrix Give a 3 by 3 matrix A such that AA#0, A² 0, and A³ = 0. Inverse and pseudo-inverse 1. Given that the inverse of AT A exists, show that A has a left pseudoinverse-that is, there exists a matrix B such that BA = I. 2. Given that the inverse of AA exists, show that A has a right pseudoinverse-that is, there exists a matrix C such that AC = I. 3. Show that if BA = I and AC = I then B = C.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do the inverse section and please show step by step and explain
Transcribed Image Text:Nilpotent matrix
Give a 3 by 3 matrix A such that A40, A² #0, and A³ = 0.
Inverse and pseudo-inverse
1. Given that the inverse of AA exists, show that A has a left pseudoinverse-that is, there exists a
matrix B such that BA = I.
2. Given that the inverse of AA exists, show that A has a right pseudoinverse—that is, there exists
a matrix C such that AC = I.
3. Show that if BA = I and AC = I then B = C.
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