GATE AG 2026 • Q15 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Solutions of linear and non-linear algebraic equations

Question Statement:

Consider the simultaneous equations 2x + 4y = −7; 3x + 5y = 1 While solving using Gauss elimination without pivoting, after the forward elimination, the diagonal elements of the coefficient matrix are

Options:

  • (A) 2 and −1
  • (B) 3 and 2
  • (C) 5 and −2
  • (D) 3 and 4

Official Answer Key:

A

Step-by-Step Solution & Explanation

Coefficient matrix: [ 2 4 ] [ 3 5 ] Pivot a₁₁ = 2 (no pivoting, so row 1 is retained as is). Multiplier m₂₁ = 3/2. R₂ → R₂ − (3/2)R₁ : a₂₁ = 3 − (3/2)(2) = 0 a₂₂ = 5 − (3/2)(4) = 5 − 6 = −1 Upper triangular matrix: [ 2 4 ] [ 0 −1 ] Diagonal elements = 2 and −1.

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