A null space is a vector space. Is this statement true or false?

A. True because the null space of an mn matrix A is a subspace of set of real numbers R^m

B. True because the null space of an mn matrix A is a subspace of set of real numbers R^n

C. False, a column space is a vector space, but a null space is not a vector space

D. False, a vector space is a null space, but a null space is not necessarily a vector space

Question

Judy

30 April, 01:36

+4

Answers (1)

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Warren Thornton · Answer 1

Let A be m*n matrix

Statement is true

Null space is a subspace of R^n and by definition, a subspace of a vector space is itself a vector space.