How to Calculate T(2, -1, 1) Using Given Linear Transformations?

[vanitymdl]

Homework Statement

Let T: R3 → R3 be a linear transformation such that T(1, 1, 1) = (1, 0, –1), T(0, – 1, 2) = (–3, 3, –1), and T(1, 0, 1) = (1, 1, 0). Find the following expression. (Enter each vector as a comma-separated list of its components.)

what is T(2, –1, 1)?

The Attempt at a Solution

So what i did was 2T(1, 1, 1)-T(0, – 1, 2)+T(1, 0, 1)
then this can be rewritten as 2(1, 0, –1)-(–3, 3, –1)+(1, 1, 0) so once I did that I got (6,-2,-1), but that is obviously the wrong answer and I don't know why.

 

[Steely Dan]

Well, your linear combination to obtain T(2,-1,1) doesn't work out, because the middle component ends up being 3, not -1.