GATE 2014 CS (CS3) – Question 15
$V_1,V_2$ are four-dimensional subspaces of a six-dimensional vector space V. Find the smallest possible dimension of $V_1\cap V_2$.
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Correct answer: 2 to 2
Explanation
The dimension identity gives dim(V1∩V2)=4+4−dim(V1+V2). The sum fits in a6dimensional space, so the intersection is at least2. Taking spans(e1,e2,e3,e4)and(e3,e4,e5,e6)attains **2**.