16. Which of the following is a basis for the subspace of R³ generated by the vectors

A	B	C
D	E Four vectors cannot span a subspace of R3

Solution The answer is B.

Start with one step of gaussian (row) reduction to the matrix

to get

This shows that subspace generated by the 4 given vectors is of dimension 2, so the only possible answer is B or C.

Next, notice that

and

So, the answer is B.