Allied & ICAR Exam Bank • ALLIED_1007 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Rank of a matrix

Question Statement:

The rank of the matrix $M = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{pmatrix}$ is:

Options:

  • (A) 0
  • (B) 1
  • (C) 2
  • (D) 3

Answer Key:

B

Step-by-Step Solution & Explanation

Rows 2 and 3 are scalar multiples of Row 1: $R_2 = 2R_1$ and $R_3 = 3R_1$. Hence, there is only 1 linearly independent row, giving $\text{rank}(M) = 1$.
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