GATE 2026 ST – Question 13

Matrix Theory · Vector Spaces and Linear Systems · 1 mark · Multiple choice

In ℝ⁴ let W₁={x:x₁+x₂+x₃+x₄=0},W₂={x:x₁+2x₂+3x₃+4x₄=0}. Find dim(W₁∩W₂).

Show answer and explanation

Correct answer: (C) 2

Explanation

The intersection is the kernel of a 2×4 matrix with independent rows (1,1,1,1),(1,2,3,4). Its rank is 2, so nullity=4−2=**2, C**.

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