Q3Single correct5 Marks10 May 2026

Let $T: \mathbb{R}^3 \to \mathbb{R}^3$ be a linear transformation given by $T(1,0,0) = (1,0,0)$, $T(1,1,0) = (0,1,0)$, and $T(0,1,1) = (0,0,1)$. Choose the correct option from the following.

A

T(x, y, z) = (x - y - z, x + y - z, -x + y + z)

B

T(x, y, z) = (x - y + z, y - z, z)

C

T(x, y, z) = (x - y - z, y - z, -x + 2y + z)

D

T(x, y, z) = (x - y + z, x - y, -z + y + z)