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GATE 2021 IN – Question 11

Engineering Mathematics · Linear algebra and matrices · 1 mark · Multiple choice

Consider row vectors $v=(1,0)$ and $w=(2,0)$. The rank of $M=2v^Tv+3w^Tw$, where $T$ denotes transpose, is ______.

  1. 1
  2. 2
  3. 3
  4. 4

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Show answer and explanation

Correct answer: (A) 1

Explanation

The outer products are vᵀv=diag(1,0) and wᵀw=diag(4,0).

Hence M=diag(14,0). There is one independent nonzero row/column, so its rank is **1, A**. The two vectors point in the same direction and do not generate rank two.