Q28Multiple correct3 Marks11 Dec 2022

Consider the affine subspaces $W_1 = \{(x, y, z) \in \mathbb{R}^3 \mid x + y + z = 1\}$ and $W_2 = \{(x, y, z) \in \mathbb{R}^3 \mid x = 3\}$. Let $V_1$ and $V_2$ be the subspaces corresponding to $W_1$ and $W_2$ respectively. Choose the correct option(s).

A

$V_1 = \text{span}\{(1, -1, 0), (0, 1, -1)\}$

B

$V_2 = \text{span}\{(1, 0, 0), (0, 1, 0)\}$

C

v_1 $\cap$ v_2 represents a plane passing through the origin in $\mathbb{R}^3$

D

v_1 $\cap$ v_2 represents a line passing through the origin in $\mathbb{R}^3$