a. If B is a basis for a subspace H, then each vector in H can be written in only one way as a linear combination of the vectors in B.

c. The dimension of *Nul A* is the number of variables in the equation $Ax= 0$

d. The dimension of the column space of A is rank A

If B

Adrian

Answered by Aaron 3 years ago

**part a**

True, the main reason for selecting a basis for a subspace H, instead of merely a spanning set, is that each vector in H can be written in only one way.

**part c**

False, the dimension of *Nul A* is the number of free variables for $Ax=0$

**part d**

True, by definition the rank is the dimension of the column space of *A*

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Asked: 3 years ago