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GATE 2022 IN – Question 24

Engineering Mathematics · Linear algebra and matrices · 1 mark · Multiple select

Given $M=\begin{bmatrix}2&3&7\\6&4&7\\4&6&14\end{bmatrix}$, which statements are correct?

  1. The rank of M is 2
  2. The rank of M is 3
  3. The rows of M are linearly independent
  4. The determinant of M is 0

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Show answer and explanation

Correct answer: (A) The rank of M is 2; (D) The determinant of M is 0

Explanation

The third row is twice the first, so determinant is zero and rank below three. The first two rows are independent, for example their first-two-column minor is 2×4−3×6=−10.

Thus rank is two and **A,D** are correct.