(d) If columns of A are linearly independent, then AA is invertible.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
D only
Transcribed Image Text:Let A be an m x n matrix over complex field.
(a) Prove that if x = N(L), then Ax is in both R(L) and N(L.).
2.
(b) Prove that N(L.) = N(L₂).
A
(c) Prove that rank(A™A) = rank(4)
(d) If columns of A are linearly independent, then A A is invertible.
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