1. Another Spanning set question

Given

x1=[-1 2 3]^T x2=[3 4 2]^T x=[2 6 6]^T y=[-9 -2 5]^T

Is x Є Span(x1,x2)?

I'm not sure where to go with this. It doesn't seem as though x1 and x2 would span R^3 but I don't know if that would be relevant or not. Any help would be appreciated, thank you!

2. Originally Posted by pakman
Given

x1=[-1 2 3]^T x2=[3 4 2]^T x=[2 6 6]^T y=[-9 -2 5]^T

Is x Є Span(x1,x2)?

I'm not sure where to go with this. It doesn't seem as though x1 and x2 would span R^3 but I don't know if that would be relevant or not. Any help would be appreciated, thank you!
What we need to know is does there exits $a,b \in \mathbb{R}$

$ax_1+bx_2=x \iff (-a,-2a+3a)+(3b,4b,2b)=(2,6,6)$

or the system

$-a+3b=2$
$-2a+4b=6$
$3a+2b=6$

The above overdetermined system is inconsistant

So x is not in the span.

I hope this helps

3. Originally Posted by pakman
Given

x1=[-1 2 3]^T x2=[3 4 2]^T x=[2 6 6]^T y=[-9 -2 5]^T

Is x Є Span(x1,x2)?

I'm not sure where to go with this. It doesn't seem as though x1 and x2 would span R^3 but I don't know if that would be relevant or not. Any help would be appreciated, thank you!
These are not consistent. This means $x \not \in \text{ Span}(x_1, x_2)$