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## Homework Statement

Given:

[tex]v_1 = \left(\begin{array}{cc}1\\-5\\-3\end{array}\right)

v_2 = \left(\begin{array}{cc}-2\\10\\6\end{array}\right)

v_3 = \left(\begin{array}{cc}2\\-9\\h\end{array}\right)

[/tex]

For what value of h is [tex]v_3[/tex] in Span{[tex]v_1, v_2[/tex]} and for what value of h is {[tex]v_1,v_2,v_3[/tex]} linearly dependent?

## Homework Equations

## The Attempt at a Solution

If my understanding is correct, a vector is in a span of another set of vectors if all vectors are in the same plane? If so then my guess is h would have to be a multiple of -3.

The linear dependence part of the question is getting me though. I was under the impression that all three vectors would have to be multiples of each other for it to be linearly dependent?