(a) Define orthogonal and idempotent matrices with examples. Prove that the only matrices which commute with an nxn matrix are the nxn scalar matrices. Compute AB ´1 2 0) by the method of conformal portioning of A by B, when A=3 1 0 and 20 1) (2 1 1 0) B =1 2 1 0 2 31 2)

(a) Define orthogonal and idempotent matrices with examples. Prove that the only matrices which commute with an nxn matrix are the nxn scalar matrices. Compute AB ´1 2 0) by the method of conformal portioning of A by B, when A=3 1 0 and 20 1) (2 1 1 0) B =1 2 1 0 2 31 2)

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 50EQ

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Question

1. (a) Define orthogonal and idempotent matrices with examples. Prove that the only
matrices which commute with an nxn matrix are the nxn scalar matrices. Compute AB
1 2 0)
by the method of conformal portioning of A by B, when A= 3 1 0 and
20 1
(2 1 1 0
B = 1 2 1 0
2 3 1 2

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