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GATE DA 2025 Q12: Cost of Gaussian elimination on an upper triangular matrix

Question

The number of additions and multiplications involved in performing Gaussian elimination on any n×nn \times n upper triangular matrix is of the order

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Answer: B (official GATE 2025 final answer key)

Concept used: Operation count of back substitution on a triangular system.

First step: An upper triangular matrix needs no forward elimination; only back substitution remains, where row ii uses about n−in - i multiplications and additions.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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