Allied & ICAR Exam Bank • ALLIED_2622 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If $v$ is an eigenvector of matrix $A$ corresponding to eigenvalue $\lambda$, then $v$ is also an eigenvector of $A^3 + 2A$ with eigenvalue:

Options:

  • (A) $\lambda^3 + 2\lambda$
  • (B) $3\lambda + 2$
  • (C) $\lambda^2 + 2$
  • (D) $\lambda^3 + 2$

Answer Key:

A

Step-by-Step Solution & Explanation

$(A^3 + 2A) v = A^3 v + 2 A v = \lambda^3 v + 2 \lambda v = (\lambda^3 + 2\lambda) v$.
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