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.
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
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