A. is (2,6,6)^t in span(x1, x2) where x1=(-1,2,3)^t and x2=(3,4,2)^t? B. is (-9,

Question

                    A. is (2,6,6)^t in span(x1, x2) where x1=(-1,2,3)^t and x2=(3,4,2)^t?                 

                                     B. is (-9,-2,5) in span(x1, x2) where x1=(-1,2,3)^t and x2=(3,4,2)^t?

I need some help! I am trying to find a way to get this but keep coming up with something that doesn't work. Let me tell you how I am approaching this and if someone could point me in the right direction, that'd be great!

I am trying to find alpha(x1) + alpha(x2)=x.

But when I do this, I get x=(2,6,5).

PLEASE HELP ME!!!

Explanation / Answer

You need to do alpha(x1)+beta(x2)=x

then solve to get alpha n beta.
in A

alpha*(-1,2,3)+beta(3,4,2)=(2,6,6)

so we get

3beta-alpha=2

4beta+2alpha = 6

so we get alpha = 1 and beta = 1

but this does not satisfy 3aplha+2 beta = 6

so A is not in the span of x1,x2

in B

alpha(x1)+beta(x2)=x

aplha = 3

beta = -2 satisfies

so B is in span of (x1,x2)

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