5. Let A be an n x k matrix for some 1 ≤ k ≤n, with real entries. 5a. Show that nul(ATA) = nul(A). 5b. Show that rank(ATA) = rank(A). 5c. Show that AT A is invertible if and only if A has independent columns.
5. Let A be an n x k matrix for some 1 ≤ k ≤n, with real entries. 5a. Show that nul(ATA) = nul(A). 5b. Show that rank(ATA) = rank(A). 5c. Show that AT A is invertible if and only if A has independent columns.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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