Allied & ICAR Exam Bank • ALLIED_0772 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Rank and determinant of matrices

Question Statement:

A $4 \times 5$ real matrix $A$ has rank equal to $3$. The nullity of matrix $A$ (dimension of the null space) is:

Answer Key:

2

Step-by-Step Solution & Explanation

By the Rank-Nullity Theorem, $\text{rank}(A) + \text{nullity}(A) = n = 5$. Thus, $\text{nullity}(A) = 5 - 3 = 2$.
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