GATE DA 2025 Set 1 — Question 12
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+1 / -0.33MediumGaussian EliminationSystems of Linear EquationsLinear AlgebraTime ComplexityComplexity AnalysisProgramming, Data Structures & Algorithms
Linear Algebra → Complexity Analysis → Gaussian Elimination
Last updated
Question
The number of additions and multiplications involved in performing Gaussian elimination on any upper triangular matrix is of the order
Correct answer
(B) O(n²)
Solution
An upper triangular matrix is already in row echelon form, so the forward-elimination phase of Gaussian elimination does no arithmetic: every multiplier for the entries below the diagonal is .The arithmetic that remains is the back substitution that solves :
- : one division.
- : multiplication, subtraction, division.
- In general needs multiplications and subtractions, plus one division.
- is too small: all nonzero entries are read at least once.
- is the cost of Gaussian elimination on a full matrix, where each of the pivot steps updates an block; for an already triangular matrix that work vanishes.
- is far larger than the actual count.
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 DA 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 Complexity Analysis
2026 Set 1 Q15Consider that the quick sort algorithm is used to sort an array of distinct randomly ordered…2026 Set 1 Q16Consider the given Python program. [code] Which of the following is the correct output of this…2026 Set 1 Q21Let be…2026 Set 1 Q22Consider a set . Let be…2026 Set 1 Q25You are given the following Pre-order and In-order traversals of a Binary Tree T with nodes E, F,…