SOLUTION: Let A be an m x n matrix. Show that if A has linearly independent column vectors, then Null(A) = 0.

SOLUTION: Let A be an m x n matrix. Show that if A has linearly independent column vectors, then Null(A) = 0.

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Question 356160: Let A be an m x n matrix. Show that if A has linearly independent column vectors, then Null(A) = 0.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Rank of column space of A = rank of A. Thus rank(A) = n (which is the number of columns of A). By the Rank-Nullity theorem, rank(A)+null(A) = n, again the number of columns of A. Therefore n + null(A) = n, and null(A) = 0.
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