determine if the given 3-vector v is in Span(v1, v2, v3).

Question

determine if the given 3-vector v is in Span(v1, v2, v3).

v=

(

0

1

3)

Answer 1

Hello! If I'm not mistaken, this is more of a linear algebra problem. (Bolded items are vectors.) Anyway, the setup should be like so:

(v1, v2, v3) c = v

If you can solve for the vector c which will have 3 elements (c1, c2, c3), then v is in the span of the 3 vectors. The way to solve for this if the matrix (v1, v2, v3) is invertible (hopefully it is) is via:

c = (v1, v2, v3) ^-1 v

If you have follow up questions, let me know!