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## Homework Statement

T4 : R3 -> R4 is defined by T4(x1, x2, x3) = (0, x1, -3 + |x1|, x1 + x2)

## The Attempt at a Solution

I know that T4(γ1x1 + γ2x2 + γ3x3) is a linear transformation IFF

γ1.T4(x1) + γ2.T4(x2) + γ3.T4(x3)

T4(λ10 + λ2x1 + λ3(-3+|x1|) = λ1.T4(0) + λ2.T4(x1) + λ3.T4(-3 + |x1|)

T4(λ2x1 + λ3(-3 + |x1|) = λ2.T4(x1) + λ3.T4(-3 + |x1|)

λ2.T4(x1) + λ3.T4(-3 + |x1|) = λ2.T4(x1) + λ3.T4(-3 + |x1|)

I get a feeling I might be comitting a circular argument with the above proof.