23. Let M be the subspace in R⁴ generated by the vectors

Let N be the subspace in R⁴ generated by the vectors

Let V be the inersection of the subspaces M and N. Which of the following pairs of vectors constitutes a basis for V?

A

B

C

D

E

Solution: The answer is B.

To see this note that all the vectors in M have a 0 in the fourth component; all the vectors in N have a 0 in the first component. Consequently, any vector that is both in M and in N must have 0s in both the first and fourth component.

By elimination, the answer must be B.