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).(c) Prove that rank(A*A) = rank(4)(d) If columns of A are linearly independent, then AA is invertible.

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Answered: Let A be an m x n matrix over complex…

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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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(L₂₁). (c) Prove that rank(A*A) = rank(4) (d) If columns of A are linearly independent, then A A is invertible.