For what values of h is v3 in span{v1,v2} and for what values of h is {v1,v2,v3} linearly dependent? v1=(1,-3,2), v2=(-3,9,-6), v3=(5,-7,h)

Question

anonymous · Answer

For a) i made a matrix of [v1 v2 v3] and for row 2 I got (0,0, 8). Does that mean that that no matter what b i select, v3 is not in span{v1,v2} ?

sriram · Answer

i guess so coz the value of x & y of V3  is  out of the range of x & y of v1 & v2 .

anonymous · Answer

ok, how about part b? I dont know how to do that one

sriram · Answer

look we can write v2=-3*v1
similarly we want a relation btwn v1 v2 & v3

anonymous · Answer

sorry, im still lost. How does that relate to seeing if the vectors are linearly dependent?