For a m x n matrix A and n x p matrix B, rank AB ≤ rank A and rank AB ≤ rank B. Use this to prove the following: (a) If P is an invertible m x m matrix, then rank PA = rank A. (b) If Q is an invertible n x n matrix, then rank AQ = rank A.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.4: The Lu Factorization
Problem 15EQ
icon
Related questions
Question
100%

Dear expert don't Use chat gpt plz 

For a m x n matrix A and nx p matrix B, rank AB ≤ rank A and rank AB < rank B.
Use this to prove the following:
(a) If P is an invertible m x m matrix, then rank PA = rank A.
(b) If Q is an invertible n x n matrix, then rank AQ = rank A.
Transcribed Image Text:For a m x n matrix A and nx p matrix B, rank AB ≤ rank A and rank AB < rank B. Use this to prove the following: (a) If P is an invertible m x m matrix, then rank PA = rank A. (b) If Q is an invertible n x n matrix, then rank AQ = rank A.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

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
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,