Allied & ICAR Exam Bank • ALLIED_0022 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The matrix $A = \begin{pmatrix} 5 & 0 \\ 0 & 5 \end{pmatrix}$ has how many linearly independent eigenvectors?

Answer Key:

2

Step-by-Step Solution & Explanation

The geometric multiplicity of eigenvalue $\lambda = 5$ is $n - \text{rank}(A - 5I) = 2 - 0 = 2$. It possesses 2 linearly independent eigenvectors.
← Previous (ALLIED_0021) Next (ALLIED_0023) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test