Please teach how to solve not just solve A matrix is idempotent if, when multiplied by itself it yields itself. That is, A is idempotent if AA = A a) When is the matrix (idempotent? 1911 b) Consider a diagonal matrix of the following form: I 0 if its diagonal elements are either 1 or 0. 0 I . Prove that such a matrix will be idempotent ann

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.3: The Inverse Of A Matrix
Problem 44EQ
icon
Related questions
Question
Please teach how to solve not just solve
A matrix is idempotent if, when multiplied by itself it yields itself. That is, A is idempotent if AA = A
a) When is the matrix (b) idempotent?
b) Consider a diagonal matrix of the following form:
if its diagonal elements are either 1 or 0.
a11
I
0
⠀ Prove that such a matrix will be idempotent
ann
Consider two matrices A, B. Assuming these are well defined for the following operations, demonstrate whether the
following operation results in a symmetric and idempotent matrix:
(AB) ((AB)'(AB))¹(AB)'
Transcribed Image Text:Please teach how to solve not just solve A matrix is idempotent if, when multiplied by itself it yields itself. That is, A is idempotent if AA = A a) When is the matrix (b) idempotent? b) Consider a diagonal matrix of the following form: if its diagonal elements are either 1 or 0. a11 I 0 ⠀ Prove that such a matrix will be idempotent ann Consider two matrices A, B. Assuming these are well defined for the following operations, demonstrate whether the following operation results in a symmetric and idempotent matrix: (AB) ((AB)'(AB))¹(AB)'
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning