Q37Comprehension2 Marks7 Aug 2022PassageBased on the above data, answer the given subquestions. Let T:R3→R3T: \mathbb{R}^3 \to \mathbb{R}^3T:R3→R3 be the linear transformation defined by T(x,y,z)=(x+2y,z−3y,x−y+z)T(x, y, z) = (x + 2y, z - 3y, x - y + z)T(x,y,z)=(x+2y,z−3y,x−y+z).Choose the correct option(s).A{(-4, 2, 6)} is a basis for the kernel of T.B{(0, 1, 3), (-2, 1, 0)} is a basis for the kernel of T.CThere exists an isomorphism from the range of T to R2\mathbb{R}^2R2.DThere exists an isomorphism from the range of T to R.
