Q44Single correct2 Marks2 Apr 2023

Consider the vector space $V=\left\{\begin{bmatrix}a&b\\a&b\end{bmatrix}:a,b\in\mathbb{R}\right\}$ and $T:\mathbb{R}^3\to V$ defined by $T(x,y,z)=\begin{bmatrix}x+y&x+y+z\\x+y&x+y+z\end{bmatrix}$. Choose the correct option.

A

$T$ is onto but not one-one.

B

$T$ is one-one but not onto.

C

$T$ is both one-one and onto.

D

$T$ is neither one-one nor onto.