GATE 2021 CS (CS2) – Question 34
P is a 4×5 matrix whose null space is spanned by [2,5,4,3,1]ᵀ. Find rank(P).
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Show answer and explanation
Correct answer: 4 to 4
Explanation
The spanning vector is nonzero, so the null space has dimension one. Rank–nullity for a matrix with five columns gives rank+nullity=5. Thus rank(P)=5−1=4, consistent with the four-row upper bound.