Prove that there exists a linear transformation $T: \mathbb R^2 \rightarrow \mathbb R^3$ such that $T(1,1)=(1,0,2)$ and $T(2,3)=(1,-1,4)$

Question

I know how to prove that a map is linear if I'm given the general rule the map is defined by. But that's not given here and I don't know how to find it from the two particular values given. Please help!

See here http://math.stackexchange.com/questions/107660/how-to-prove-there-exists-a-linear-transformation — Matthew Cassell, Jan 08 '15 at 15:29

score 3 · Accepted Answer · answered Jan 08 '15 at 15:32

3

Hints:

1) $T(1,0)=3T(1,1)-T(2,3)$

2) $T(0,1)=T(2,3)-2T(1,1)$

3) $T(a,b)=aT(1,0)+bT(0,1)$

answered Jan 08 '15 at 15:32

voldemort

13,182

Prove that there exists a linear transformation $T: \mathbb R^2 \rightarrow \mathbb R^3$ such that $T(1,1)=(1,0,2)$ and $T(2,3)=(1,-1,4)$

1 Answers1