Linear algebra Let v1 1 1 v2 2 1 3 v3 4 2 6 and w 3 1 2

Let v_1 = [1 ! -1], v_2 = [2 1 3], v_3 = [4 2 6], and w = [3 1 2] Is w in {v_1, v_2, v_3)? How many vectors are in {v_1. v_2. v_3}? How many vectors are in Span{v_1, v_2, v_3}? Is win the subspace spanned by {v_1, v_2. v_3}? Why? Is lambda = 4 an eigenvalue of [3 0 -1 2 3 1]? If so, find one corresponding

Solution

a.

No. We can see that by just looking at v1,v2,v3 to see if w is one of them

b.

Infinitely many as v1,v2,v3 are non zero vectors and span consists of all possible linear combinations of v1,v2,v3

c)

Yes,

w=v1+v2