Q7Numerical6 Marks21 Dec 2025Consider R4\mathbb{R}^4R4 with the usual inner product and a subspace W=span{(2,0,2,0),(0,−3,−3,0),(1,1,2,1),(4,0,4,−3)}W = \text{span}\{(2, 0, 2, 0), (0, -3, -3, 0), (1, 1, 2, 1), (4, 0, 4, -3)\}W=span{(2,0,2,0),(0,−3,−3,0),(1,1,2,1),(4,0,4,−3)} of R4\mathbb{R}^4R4. Define W⊥={v∈R4∣w⋅v=0 for all w∈W}W^\perp = \{v \in \mathbb{R}^4 \mid w \cdot v = 0 \text{ for all } w \in W\}W⊥={v∈R4∣w⋅v=0 for all w∈W}. What is the dimension of W⊥W^\perpW⊥?Your answerPress Enter to check.
