GATE 2019 AE – Question 42
Engineering Mathematics · Linear Algebra: Vector algebra, matrix algebra, systems of linear equations, rank, eigenvalues and eigenvectors · 2 marks · Numerical answer
One eigenvalue of $A=\begin{pmatrix}x&2\\-1&3\end{pmatrix}$ is 1. Find its other eigenvalue.
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Correct answer: 2 to 2
Explanation
Set det(A−I)=0: $2(x-1)+2=2x=0$, so x=0. The trace is then 3 and equals the sum of the eigenvalues. The remaining eigenvalue is 3−1=2.
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