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GATE 2026 Chemical Engineering, Q23 · Mathematics

The correct answer is B, −5, 5.

Question

Which one of the following is the pair of eigenvalues of the matrix [[−3, 4], [4, 3]]?

  • A. −7, 7
  • B. −5, 5
  • C. −4, 3
  • D. −3, 4

Official answer: −5, 5

Why

GATE 2026 official key: (B). The matrix is symmetric, so eigenvalues are real: det([[−3−λ,4],[4,3−λ]])=λ2−25=0det([[−3−λ,4],[4,3−λ]]) = λ² − 25 = 0 → λ=±5λ = \pm 5 (check: trace = 0 = −5+5 ✓, det =−25=−5×5= −25 = −5 \times 5 ✓).

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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