GATE CE 2025 Set 1 — Question 11
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33EasyEigenvalues & EigenvectorsLinear AlgebraEngineering Mathematics
Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
Last updated
Question
Suppose is an eigenvalue of matrix and is the corresponding eigenvector. Let also be an eigenvector of the matrix , where is the identity matrix. Then, the eigenvalue of corresponding to the eigenvector is equal to
Correct answer
(D) λ - 2
Solution
Given that is an eigenvalue of with eigenvector , we have .
For the matrix , we can find its eigenvalue corresponding to as follows:Thus, the eigenvalue of corresponding to the eigenvector is .
For the matrix , we can find its eigenvalue corresponding to as follows:Thus, the eigenvalue of corresponding to the eigenvector is .
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.