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GATE 2021 AG – Question 50

Engineering Mathematics · Linear Algebra · 2 marks · Numerical answer

Find sum of eigenvalues of $\begin{pmatrix}4&1\\3&6\end{pmatrix}$,rounded to an integer.

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Correct answer: 10 to 10

Explanation

The sum of eigenvalues counted with multiplicity equals trace. Trace=4+6=**10**. As a check, the characteristic polynomial is λ²−10λ+21,whose roots are3 and 7,again summing to 10.

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