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## Homework Statement

Show that the given set is linearly dependent and write one of the vectors as a linear combination of the remaining vectors.

{(1,2,1,0), (3,-4,5,6), (2,-1,3,3), (-2,6,-4,-6) }

## Homework Equations

## The Attempt at a Solution

I've tried setting up equations like

(0,0,0,0) = c1 * (1,2,1,0) + c2 * (3,-4,5,6) + c3 * (2,-1,3,3) + c4 * (-2,6,-4,-6)

0 = c1 + 3c2 + 2c3 - 2c4 ... etc

Unfortunately each time I try to solve them, I keep on getting 0 = 0.

But I've noticed that if I set the constant (c3) in front of the third vector (v3) in the set to 0 then it works.

v4-v1 + v2 = (0,0,0,0). Is that a valid way to answer this question? Can I set one of the constants to 0?

And if so, why can't I just set all the constants to 0 and be done with it?

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