GATE 2024 MA – Question 30

Linear Algebra · Vector Spaces and Linear Transformations · 1 mark · Numerical answer

In ℝ⁴ with standard inner product, W₁=span{(1,0,0,−1)} and W₂=span{(2,1,0,−1)}. Find dim(W₁⊥∩W₂⊥).

Show answer and explanation

Correct answer: 2 to 2

Explanation

The generating vectors are independent, so W₁+W₂ has dimension 2. Their common orthogonal complement equals (W₁+W₂)⊥ and has dimension 4−2=**2**.

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