- #1

peripatein

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## Homework Statement

How may I find (or prove that there isn't) a linear transformation which satisfies T: R

^{3}->R

_{1}[x], ker T = Sp{(1,0,1), (2,-1,1)}?

## Homework Equations

## The Attempt at a Solution

I am not sure how to approach this. I understand that kerT is the group of all vectors (x,y,z) in R

^{3}so that T(x,y,z) = 0 = Sp{(1,0,1), (2,-1,1)}. So x = alpha, y = -beta, z = alpha + beta? Hence, x,y,z=0? Hence, T has to be one-to-one? Since dim(R

_{1}[x]) is 2, does that mean that there is no such linear transformation?