# Find a linear transformation

• Feb 1st 2008, 07:37 AM
Find a linear transformation
Is there a linear transformation $T:R^3 \rightarrow R^2$ such that T(1,0,3) = (1,1) and T(-2,0,-6) = (2,1)?

I set the system of 1x+3y = 1 and -2x + -6y = 2 in an attempt to find x and y, but it turns out to be no solution, does that means there is no linear transformation in this case?
• Feb 1st 2008, 07:40 AM
topsquark
Quote:

Is there a linear transformation $T:R^3 \rightarrow R^2$ such that T(1,0,3) = (1,1) and T(-2,0,-6) = (2,1)?

I set the system of 1x+3y = 1 and -2x + -6y = 2 in an attempt to find x and y, but it turns out to be no solution, does that means there is no linear transformation in this case?

Sounds about right to me. :)

-Dan
• Feb 1st 2008, 10:34 AM
(-2)(1,0,3) = (-2,0,-6) but then (-2)T(x) $\neq$ T(-2x).