Q1Single correct2 Marks13 Jul 2025

Consider the following statements about the function $T:\mathbb{R}^2\to\mathbb{R}$ defined by $T(x,y)=2x+y+1$, for all $(x,y)\in\mathbb{R}^2$. Statement $P$: $T$ is a linear transformation. Statement $Q$: $T$ is a one-to-one (injective) map. Choose the correct option from the following.

A

Both $P$ and $Q$ are true.

B

$P$ is true and $Q$ is false.

C

$P$ is false and $Q$ is true.

D

Both $P$ and $Q$ are false.