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GATE 2017 ME (ME2) – Question 13

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Numerical answer

A 2×2 matrix has determinant 50. If one eigenvalue is 10, the other is ______.

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Correct answer: 5 to 5

Explanation

The determinant equals the product of the eigenvalues, including multiplicity. Thus10λ=50, giving **λ=5**. The sum of the eigenvalues would instead equal the trace.