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GATE 2021 CE (CE2) – Question 12

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

Find rank of $\begin{bmatrix}5&0&-5&0\\0&2&0&1\\-5&0&5&0\\0&1&0&2\end{bmatrix}$.

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

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Correct answer: (C) 3

Explanation

The third row is the negative of the first. Rows two and four are independent because their nonzero 2×2 block has determinant $2(2)-1(1)=3$. The first row is independent of those two because it occupies different columns. Thus rank is **3 (C)**.