Q12Comprehension1 Mark13 Apr 2025PassageBased on the above data, answer the given subquestions. Let v1=(−1,1,−1)v_1 = (-1, 1, -1)v1=(−1,1,−1), v2=(2,0,2)v_2 = (2, 0, 2)v2=(2,0,2), v3=(1,−2,1)v_3 = (1, -2, 1)v3=(1,−2,1), and W=span{v1,v2,v3}W = \text{span}\{v_1, v_2, v_3\}W=span{v1,v2,v3}.Let U={(x,y,z)∈R3∣x+y+z=0}U = \{(x, y, z) \in \mathbb{R}^3 \mid x + y + z = 0\}U={(x,y,z)∈R3∣x+y+z=0}. Which of the following sets represents W∩UW \cap UW∩U?Aspan{(1,0,1)}\text{span}\{(1, 0, 1)\}span{(1,0,1)}Bspan{(1,2,1)}\text{span}\{(1, 2, 1)\}span{(1,2,1)}C{(x,y,z)∈R3∣2x=−y=2z}\{(x, y, z) \in \mathbb{R}^3 \mid 2x = -y = 2z\}{(x,y,z)∈R3∣2x=−y=2z}D{(x,y,z)∈R3∣x=−2y=z}\{(x, y, z) \in \mathbb{R}^3 \mid x = -2y = z\}{(x,y,z)∈R3∣x=−2y=z}
