GATE EC 2016 Set 3 — 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
Consider a square matrix where x is unknown. If the eigenvalues of the matrix A are and , then x is equal to
Correct answer
(D) -ω
Solution
The eigenvalues of a matrix are given by the characteristic equation .
For the given matrix , the characteristic equation is:
We are given that the eigenvalues are and .
Comparing these with , we have:
Squaring both sides:
If , we can divide by :
Therefore, the correct option is (D).
For the given matrix , the characteristic equation is:
We are given that the eigenvalues are and .
Comparing these with , we have:
Squaring both sides:
If , we can divide by :
Therefore, the correct option is (D).
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 EC 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.
More questions on Linear Algebra
2026 Set 1 Q11Consider the differential equation , with…2026 Set 1 Q12A surface is given by and and are unit…2026 Set 1 Q23The relation between the input current () and the output voltage () of a circuit is governed…2026 Set 1 Q26Consider the matrix . Which…2026 Set 1 Q36Consider the two series, and , where …