Question

Linear algebra question

Answer 1

I kind of have an idea on how to do this but I am not 100% sure.

Answer 2

Show me what you got, and I'll help you figure it out.

Answer 3

Try writing this as a linear combination of column vectors.

Answer 4

And we'll go from there and convert it over to an augmented matrix.

Answer 5

Just some reasoning. I substituted for u and v with the given vectors and made it not equal to 0.

Answer 6

\[x1(0,1,1)+x2(0,1,1)+x3(t,2,-1)\neq(0,0,1)\]

Answer 7

That's basically it at this point.

Answer 8

I am stuck here. Unless my theory was wrong.

Answer 9

You're on the right track, but at this point you're sort of still solving for t. I'd set it up more like this and say they're equal for now and then look at what I get from there. I'll show you:

\[\left[\begin{matrix}1 & 0 & t &0\\ 1 & 1 & 2 &0\\ -2 & 1 & -1 &1\end{matrix}\right]\]

So this is the augmented matrix, and then I'd try playing around with this and then say that whatever comes up is not equal to get a more general answer.

Answer 10

Well apparently t=1 . It's not a general answer.

Answer 11

I would get this to RREF right?

Answer 12

t can equal 1, but it can also equal a lot of other things to satisfy this requirement. What you need to do is get this in RREF to solve for all three values of t that do not work.

Answer 13

Right.

Answer 14

One second.

Answer 15

After you get your answers for t, you can plug them into your matrix, put it in RREF and it will tell you what scalars to put on each of the 3 vectors to get <0,0,1>. Since this is what you don't want, you know you're good because you just plugged in t which is what you don't want. I hope that isn't too many negatives. =D

Answer 16

Well I got :