Find eigenvalues of pmatrix1&2&3\\0&4&7\\0&0&3pmatrix.

GATE 2011 CS (CS1) – Question 50

Engineering Mathematics · Linear Algebra · 2 marks · Multiple choice

Find eigenvalues of $$\begin{pmatrix}1&2&3\\0&4&7\\0&0&3\end{pmatrix}.$$

1,4,3
3,7,3
7,3,2
1,2,3

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Show answer and explanation

Correct answer: (A) 1,4,3

Explanation

For an upper-triangular matrix, det(λI−A) is the product of its diagonal factors, (λ−1)(λ−4)(λ−3). Therefore eigenvalues are diagonal entries 1,4,3, option A.

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