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GATE 2026 AG – Question 15

Engineering Mathematics · Numerical Methods · 1 mark · Multiple choice

For $2x+4y=-7$ and $3x+5y=1$,Gauss elimination is performed without pivoting. What diagonal entries remain after forward elimination?

  1. 2 and −1
  2. 3 and 2
  3. 5 and −2
  4. 3 and 4

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Correct answer: (A) 2 and −1

Explanation

The initial coefficient matrix is \begin{pmatrix}2&4\\3&5\end{pmatrix}. Keep the first pivot 2 and replace row 2 by row 2 minus $3/2$ of row 1. The second diagonal entry becomes $5-(3/2)4=-1$. Hence the diagonal is **2,−1; A**.

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