Q7Single correct5 Marks21 Dec 2025

Let $T: \mathbb{R}^2 \to \mathbb{R}^2$ be the linear transformation $T(x, y) = (2x + y, 3x + y)$ and $A$ denote the matrix representation of $T$ with respect to the ordered basis $\{(1, 0), (0, 1)\}$ of domain and $\{(1, 1), (-1, 1)\}$ of co-domain. Consider the following statements. S1: $A$ is similar to $\begin{bmatrix} 5 & 2 \\ 1 & 0 \end{bmatrix}$. S2: $A$ is equivalent to $\begin{bmatrix} 5 & 2 \\ 1 & 0 \end{bmatrix}$. Choose the correct option.

A

Both the statements S1 and S2 are true.

B

Only statement S1 is true.

C

Only statement S2 is true.

D

Both the statements are false.