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GATE 2018 ME (ME1) – Question 12

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

Find the rank of $$\begin{bmatrix}-4&1&-1\\-1&-1&-1\\7&-3&1\end{bmatrix}$$.

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

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Correct answer: (B) 2

Explanation

The determinant is zero. The first two rows are independent: their first-two-column minor is $(-4)(-1)-1(-1)=5\ne0$. Thus rank is at least 2 but below 3, hence 2 (B).