The larger of the two eigenvalues of the matrix 4 & 5 2 & 1 is …

Official answer: 6. Explanation: Given the matrix: A = 4 & 5 2 & 1 The characteristic equation is given by det(A - I) = 0: 4 - & 5 2 & 1 - = 0 (4 - )(1 - ) - (5)(2) = 0 2 - 5 + 4 - 10 = 0 2 - 5 - 6 = 0 ( - 6)( + 1) = 0 The eigenvalues are 1 = 6 and 2 = -1. The larger of the two eigenvalues is 6 [6].

Linear Algebra

GATE CSE 2015 Set 2 · Q5

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The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is ______.

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Official answer: 6

Linear Algebra

Given the matrix:

A = \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}

The characteristic equation is given by $\det(A - \lambda I) = 0$ :

\begin{vmatrix} 4 - \lambda & 5 \\ 2 & 1 - \lambda \end{vmatrix} = 0

(4 - \lambda)(1 - \lambda) - (5)(2) = 0

\lambda^2 - 5\lambda + 4 - 10 = 0

\lambda^2 - 5\lambda - 6 = 0

(\lambda - 6)(\lambda + 1) = 0

The eigenvalues are $\lambda_1 = 6$ and $\lambda_2 = -1$ .

The larger of the two eigenvalues is 6 [6].

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This Linear Algebra previous year question is Q5 of the GATE CSE 2015 Set 2 paper. Find more GATE CSE PYQs on Linear Algebra in Engineering Mathematics, or browse all GATE CSE PYQs.

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Linear Algebra in GATE CSE

Linear Algebra has 46 GATE CSE PYQs across 26 papers from 2011 to 2026. 13 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2015 Set 2.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.