Q17Multiple correct2 Marks3 Sep 2023

Let W = {(x, y, z) in $\mathbb{R}^3$ : 2x - y - z = 3}. Then which of the following affine subspace(s) of $\mathbb{R}^3$ is/are same as the subspace W?

A

$(6, 0, 0)$ + U where U = {(x, y, z) in $\mathbb{R}^3$ : 2x = y + z}

B

$(0, -3, 0)$ + U where U = {(x, y, z) in $\mathbb{R}^3$ : y = 2x - z}

C

$(0, 0, -3)$ + U where U = {(x, y, z) in $\mathbb{R}^3$ : z = 2x - y}

D

$(0, -3, 0)$ + U where U = {(x, y, z) in $\mathbb{R}^3$ : 2x = y - z}