GATE EC 2016 Set 2 — Question 39
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0EasyMatrix AlgebraLinear AlgebraEngineering MathematicsDeterminants
Engineering Mathematics → Linear Algebra → Determinants
Last updated
Question
The matrix has and .
The value of is ________
The value of is ________
Correct answer
2.9 to 3.1
Solution
For the given matrix , we use the properties of the determinant and trace.
Given , we have .
1.Determinant: The matrix is a block-triangular-like matrix. We can find the determinant by expanding along the last row:
Expanding the matrix along its last row:Thus, .Given , we have .
2.Trace: The trace of a matrix is the sum of its diagonal elements:
Given , we have .3.Calculation of : We use the algebraic identity :
The value is 3, which falls within the specified range of 2.9 to 3.1.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 …