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GATE 2025 MN – Question 55

Engineering Mathematics · Linear Algebra · 2 marks · Numerical answer

The characteristic polynomial is $x^3-6x^2+11x-6$. One eigenvalue is1. Find the sum of the other two,as an integer.

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Correct answer: 5 to 5

Explanation

The sum of all three eigenvalues equals6,from the negative coefficient of x² in the monic characteristic polynomial. Subtract the known eigenvalue1 to obtain5. Equivalently,the polynomial factors as(x−1)(x−2)(x−3).

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