Linear Transformation: Finding a Solution for a System of Linear Equations

[stunner5000pt]

Find a linear transformation with the given properties

T(2,-1) = (1,-1,1) and T(1,1) = (0,1,0)

we need to find an expression for t(x,y)
so we could find what linear combo on (2,-1) and (1,1) yierlds x,y
But i tried that and i find that i cannot solve this system of linear equations with a consistent solution
2a + b = x
-a + b = y
it doesn't work...

Please help!

 

[nocturnal]

so we could find what linear combo on (2,-1) and (1,1) yierlds x,y
But i tried that and i find that i cannot solve this system of linear equations with a consistent solution
2a + b = x
-a + b = y
it doesn't work...

really? show what you've done so we can see what went wrong.

 

[Euclid]

It is enough to find a linear combination of (2,-1) and (1,1) that eliminates one of the components:
(2,-1) - 2(1,1) = (0,-3)
This should tell you how T acts on (0,1) and hence (0,y).
You can do the same for the other component.