I'm confused on this question steps would help Let A and B two matrices of order n x n. Prove the follwoing claims:(a) N(A)nN(B) CN(A + B).(b) N(B) C N(AB)(c) R(AB) C R(A)Where N(A) represents the nullspace of A and and R(B) range of B.

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Answered: Let A and B two matrices of order n x…

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 and B two matrices of order n x n. Prove the follwoing claims: (a) N(A)NN(B) CN(A+ B). (b) N(B) C N(AB) (c) R(AB) C R(A) Where N(A) represents the nullspace of A and and R(B) range of B.