GATE CS 2025 Set 1 — Question 23
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+1 / -0MediumSystem of Linear EquationsLinear AlgebraEngineering Mathematics
Engineering Mathematics → Linear Algebra → System of Linear Equations
Last updated
Question
Consider the given system of linear equations for variables and , where is a real-valued constant. Which of the following option(s) is/are CORRECT?
Correct answer
(A) There is exactly one value of k for which the above system of equations has no solution.; (D) There exists exactly one value of k for which the system of equations has an infinite number of solutions.
Solution
The system can be written as where and .
The determinant is .
The determinant is .
- Case 1: . The system has a unique solution. Since there are infinitely many such , option (C) is false.
- Case 2: . The equations are and . These are parallel lines with no intersection. Thus, no solution. This is the only value for no solution, so (A) is true and (B) is false.
- Case 3: . The equations are and . These are the same line, so there are infinite solutions. This is the only value for infinite solutions, so (D) is true.
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 CS 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 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…