GATE 2017 CE (CE2) – Question 11

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Consider $3x_1+2x_2=c_1$ and $4x_1+x_2=c_2$, where $c_1,c_2$ are constants. The characteristic equation of the coefficient matrix is ______.

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

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Correct answer: (A) $\lambda^2-4\lambda-5=0$

Explanation

The characteristic polynomial is $\det(A-\lambda I)=(3-\lambda)(1-\lambda)-8=\lambda^2-4\lambda-5$. Its trace is 4 and determinant is −5, confirming the coefficients. Answer A.