GATE AG 2020 • Q24 NAT • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If one of the two eigenvalues of the matrix $\begin{bmatrix} 3 & 2 \\ 2 & 1 \end{bmatrix}$ is 4.236, find the other eigenvalue. (Rounded to 3 decimal places)

Official Answer Key:

0.236

Step-by-Step Solution & Explanation

Sum of eigenvalues = trace of matrix = 3+1 = 4. Other eigenvalue = 4 − 4.236 = −0.236.

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