Linear Algebra- Linear Transformations

[FinalStand]

Homework Statement

Let T: R3--> R4 be a linear transformation. Assume that T(1,-2,3) = (1,2,3,4), T(2,1,-1)=(1,0,-1,0)
Which of the following is T(-8,1-3)?

A. (-5,-4,-3,-8)
B. (-5,-4,-3,8)
C. (-5,-4,3,-8).
D.(-5,4,3,-8)
E (-5,4,-3,8)
F. None of the above.

Homework Equations

I really have no clue how to solve this problem. All I know is how to verify if it is linear transformation or not by verifying T(u+v) = T(u) + T(v) and cT(u) = T(c(u)).
And that T(x) = Ax and also that T(0)=0

The Attempt at a Solution

I tried applying those above but nothing works for me. To be honest I have no clue how to start, I tried to find patterns but failed to identify any. Any hints?

Thanks

 

[vela]

You can combine those two conditions for linearity and say ##T(r\vec{u}+s\vec{v}) = rT(\vec{u}) + sT(\vec{v})##. Try think how that might be useful in light of the information you've been given about T.

 

[FinalStand]

I got something like T(r+2s, -2r+s, 3r-s) = (r+s, 2r, 3r-s, 4r) Then the answer could be A. But how do you actually do the question how tdo you solve that? I just did by guessing and inputing numbers to get one of the choices (A-F).

 

[FinalStand]

Oh I got it, you just have to set the T(...) = T(-8,1,-3) :D

 

[vela]

Yup.