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GATE 2017 EC – Question 12

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

The rank of the matrix $M = \begin{bmatrix} 5 & 10 & 10 \\ 1 & 0 & 2 \\ 3 & 6 & 6 \end{bmatrix}$ is

  1. 0
  2. 1
  3. 2
  4. 3

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Correct answer: (C) 2

Explanation

The first row $(5, 10, 10)$ is $\frac{5}{3}$ times the third row $(3, 6, 6)$, so they are dependent. The second row $(1, 0, 2)$ is not a multiple of them, so there are exactly 2 independent rows, and the rank is 2.