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

# 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

A
Asked by 3 years ago
45 points

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

### 1 Answer

Answered by 3 years ago
8.7k points

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