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GATE 2018 CE (CE2) – Question 38

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Multiple choice

Find the rank of $$\begin{bmatrix}1&1&0&-2\\2&0&2&2\\4&1&3&1\end{bmatrix}$$.

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

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Correct answer: (B) 2

Explanation

The third row equals the first plus 1.5 times the second. The first two rows are not proportional and are independent. Therefore exactly two rows are independent: rank 2 (B).