Computer Science and Information Technology
GATE CSE concept:eigenvalues PYQs
Build your understanding with focused practice from past exam papers.
How to practice concept:eigenvalues
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–5 of 5. Imported answers require independent review unless marked reviewed.
Question 41
Open questionCSMCQ2 marksNeeds review
Let
be a
matrix as given.
What are the eigenvalues of the matrix
?Your answerChoose one option.
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Open questionCS1MCQ1 markNeeds review
The product of all eigenvalues of the matrix
isYour answerChoose one option.
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Open questionCSNAT1 markNeeds review
Let
be the adjacency matrix of the graph with vertices
. 
Let
and
be the five eigenvalues of
. Note that these eigenvalues need not be distinct. The value of
________.Log in to check the answer
You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 31
Open questionCSMCQ2 marksNeeds review
Let
be an
real valued square symmetric matrix of rank 2 with
. Consider the following statements.(I) One eigenvalue must be in
(II) The eigenvalue with the largest magnitude must be strictly greater than 5Which of the above statements about eigenvalues of
is/are necessarily CORRECT?Your answerChoose one option.
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You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answerQuestion 52
Open questionCSNAT2 marksNeeds review
If the characteristic polynomial of a
matrix
over
(the set of real numbers) is
,
, and one eigenvalue of
is 2, then the largest among the absolute values of the eigenvalues of
is __________.Log in to check the answer
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