GATE 2026 ST – Question 26

Matrix Theory · Inner Products and Quadratic Forms · 1 mark · Numerical answer

In ℝ⁴ let U={x:x₁+x₂+x₄=0,x₃=0}. Find dim U⊥ (integer).

Show answer and explanation

Correct answer: 2 to 2

Explanation

The two independent linear constraints give dim U=4−2=2. Its orthogonal complement is spanned by their normals (1,1,0,1),(0,0,1,0), so **dim U⊥=2**.

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