GATE EE 2014 Set 1 — Question 56
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
A system matrix is given as follows.The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
Correct answer
2.9 to 3.1
Solution
To find the eigenvalues of matrix , we solve the characteristic equation .
Trace of .
Determinant of .
Sum of products of eigenvalues taken two at a time:
.
The characteristic equation is :The roots of this equation are .
The absolute value of the ratio of the maximum eigenvalue (magnitude) to the minimum eigenvalue (magnitude) is:
Trace of .
Determinant of .
Sum of products of eigenvalues taken two at a time:
.
The characteristic equation is :The roots of this equation are .
The absolute value of the ratio of the maximum eigenvalue (magnitude) to the minimum eigenvalue (magnitude) is:
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