Question: Let A be an m n matrix. (a) If B is a nonsingular m in matrix, show that BA and A have the

Let A be an m × n matrix.
(a) If B is a nonsingular m × in matrix, show that BA and A have the same nullspace and hence the same rank.
(b) If C is a nonsingular n × n matrix, show that AC and A have the same rank.

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a If x NA then BAx B0 0 and hence x NBA Thus NA is a subspace of NBA On the other hand if x ... View full answer

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