Question

Dene T : R3 ! R4 by the equation T(x1; x2; x3) = (x1

Answer 1

To determine the matrix, apply the transformation to the canonical basis vectors \(e_{1,2,3}\) and use these outputs as columns.

Answer 2

To determine whether it's one-to-one, I suggest you check how many vectors satisfy \(T(\mathbb{x})=0\) (i.e. look at the null-space/kernel). Linearity can be demonstrated pretty easily so I'll leave that to you.