Q1Single correct4 Marks15 Mar 2026Consider a subspace W={(x,y,z,w)∈R4∣x+y+z=0, y+z=w}W=\{(x,y,z,w)\in\mathbb{R}^4\mid x+y+z=0,\;y+z=w\}W={(x,y,z,w)∈R4∣x+y+z=0,y+z=w} of R4\mathbb{R}^4R4. Which of the following options describes a basis of WWW?A{(−4,1,3,4),(0,−5,5,0)}\{(-4,1,3,4),(0,-5,5,0)\}{(−4,1,3,4),(0,−5,5,0)}B{(1,−1,0,−1),(0,1,−1,0),(−1,0,1,1)}\{(1,-1,0,-1),(0,1,-1,0),(-1,0,1,1)\}{(1,−1,0,−1),(0,1,−1,0),(−1,0,1,1)}C{(−3,1,2,3),(−1,1,0,1),(0,−1,1,0)}\{(-3,1,2,3),(-1,1,0,1),(0,-1,1,0)\}{(−3,1,2,3),(−1,1,0,1),(0,−1,1,0)}D{(0,12,−12,0),(0,−3,3,0)}\{(0,\tfrac{1}{2},-\tfrac{1}{2},0),(0,-3,3,0)\}{(0,21,−21,0),(0,−3,3,0)}
