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.
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.
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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Transcribed Image Text: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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