- #1

CookieSalesman

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## Homework Statement

True or false.

If v1... v4 are linearly independent vectors in 4D space, then {v1,v2,v3} is also linearly independent.

There's a hint: Think about (c for different constant) cv1+cv2+cv3+0*v4=0

I know that linear independence means there's only the trivial solution... which means that the only constants or "weights" on vectors v1 through v4 are all zero.

But if you don't regard v4, can't the situation change?

Or also... what does this "hint" suggest" I thought that this could mean that the problem could be false...?Please just explain the reasoning...

I guess this all has to be linearly independent... because as is already said, the only weights possible are zero, right? But I'm confused. If you're saying v1 through v4 are linearly indep., the fact that they only have the trivial solution is only because v4 is there as well. If you just solve with v1 v2 v3, doesn't that change the problem...?I'm confused.

(No, I didn't use the template, but then again it didn't really apply, and so I tried to use it in spirit)