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

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

Respuesta :

JayDilla

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.

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