Q21Single correct2 Marks4 Aug 2024

Let $A=\begin{bmatrix}x&-4\\3&y\end{bmatrix}$ and $T:\mathbb{R}^2\to\mathbb{R}$ be the linear transformation given by $T(x,y)=\operatorname{trace}(A)$. Which statement is true?

A

$T$ is injective but not surjective.

B

$T$ is surjective but not injective.

C

$T$ is an isomorphism.

D

$T$ is neither injective nor surjective.