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GATE 2025 CH – Question 45

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Numerical answer

Consider the matrix $\mathbf{A} = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$

The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).

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Correct answer: 3.71 to 3.75

Explanation

The trace is 4 and the determinant is $4 - 3 = 1$, so $\lambda^2 - 4\lambda + 1 = 0$ and $\lambda = 2 \pm \sqrt{3}$, that is 0.27 and 3.73.