a) Define $T : R^2 \to R^2$ as $T(x,y) = (2x - 3y, x+y)$ for any $x,y…

Question

a) Define $T : R^2 \to R^2$ as $T(x,y) = (2x - 3y, x+y)$ for any $x,y \in R$. Then show that T is linear and also find the matrix associated with T relative to basis set $B = [e_1, e_2]$, where $e_1 = (1, 0)$ and $e_2 = (0, 1)$.

b) Let T be a linear transformation from a vector space V into itself then show that T is invertible if and only if T is one one and onto.

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