Question

v1 = (3,2,1) and v2 = (0,3,4). I know the collection [v1,v2] is linearly independent. To check v3=(1,0,0) is not in the span(v1,v2) I need to prove the matrix of v1,v2 * x = v3. But when I preform row reduction im not sure if its inconsistent! Any help appriciated.

Answer 1

if the det(A) = 0, the vectors are DEpendant, if det(A) not= 0, the vectors or INdependant

Answer 2

-(3+0+0)
3 0 1 3 0
2 3 0 2 3
1 4 0 1 4
+(0+0+8)

8-3 not= 0

Answer 3

if the rref produces a row of zeros, then you the vectors are DEpendant

ideally, you get a rref that is the identity matrix when they are INdependant