Q2Single correct5 Marks10 May 2026

Let $T: \mathbb{R}^3 \to \mathbb{R}^2$ be a linear transformation defined by $T(x, y, z) = (x - 2y, y - 3z)$. Let $B_1 = \{(1, 0, 1), (1, 1, 0), (0, 1, 1)\}$ and $B_2 = \{(1, 1), (1, -1)\}$ be ordered bases. Choose the correct option for the matrix representation of $T$ with respect to ordered bases $B_1$ for the domain and $B_2$ for the co-domain.

A

$\begin{bmatrix} 1 & 0 & -2 \\ -2 & -1 & 0 \end{bmatrix}$

B

$\begin{bmatrix} -1 & 0 & -2 \\ 2 & -1 & 0 \end{bmatrix}$

C

$\begin{bmatrix} -1 & 0 & -2 \\ 2 & 1 & 0 \end{bmatrix}$

D

$\begin{bmatrix} -1 & 0 & 2 \\ 2 & -1 & 0 \end{bmatrix}$