Linear algebra question

Question

Show that the following sets of vectors of R3 are linearly independentand span R3:

(a) S1 = {(1, 2, 3),(3, 2, 1),(0, 0, 1)}.

(b) S2 = {(3, 0, −6),(−4, 1, 7),(−2, 1, 5)}.

Answer 1

(a) The easiest way (in my opinion) to do this is to compute the determinant of the matrix

1 2 3

3 2 1

0 0 1

If the determinant is nonzero, the vectors are linearly independent and thus form a basis for R3.

(b) Exact same process.