Allied & ICAR Exam Bank • ALLIED_0008 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

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

Answer Key:

1

Step-by-Step Solution & Explanation

Row 2 and Row 3 are linear scalar multiples of Row 1. Hence, the matrix has only 1 linearly independent row, so $\text{Rank}(A) = 1$.
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