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GATE 2021 CE (CE1) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

The rank of the matrix $\begin{bmatrix}1&2&2&3\\3&4&2&5\\5&6&2&7\\7&8&2&9\end{bmatrix}$ is

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

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Correct answer: (B) 2

Explanation

Every successive row differs by $(2,2,0,2)$, so all rows lie in the span of the first row and this difference vector. These two vectors are independent: the first has third component 2 while the difference has third component 0. The rank is **2 (B)**.