Electronics and Communication Engineering
GATE ECE topic:linear-algebra PYQs
Build your understanding with focused practice from past exam papers.
Questions 11–20 of 21. Imported answers require independent review unless marked reviewed.
Question 16
Open questionECNAT1 markNeeds review
If the vectors
,
and
in
are linearly dependent, the value of
is __________.Log in to check the answer
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Open questionECNAT2 marksNeeds review
A real
non-singular matrix
with repeated eigenvalue is given as
where
is a real positive number. The value of
(rounded off to one decimal place) is ________.Log in to check the answer
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Open questionECMCQ1 markNeeds review
If
are six vectors in
, which one of the following statements is FALSE?Your answerChoose one option.
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Open questionECMCQ2 marksNeeds review
Consider the following system of linear equations.
Which one of the following conditions ensures that a solution exists for the above system?Your answerChoose one option.
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Open questionECNAT1 markNeeds review
The number of distinct eigenvalues of the matrix
is equal to ______.Log in to check the answer
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Open questionECMCQ1 markNeeds review
Let M be a real
matrix. Consider the following statements:S1: M has 4 linearly independent eigenvectors.
S2: M has 4 distinct eigenvalues.
S3: M is non-singular (invertible).
Which one among the following is TRUE?
Your answerChoose one option.
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Open questionECNAT1 markNeeds review
Consider matrix
and vector
. The number of distinct real values of
for which the equation
has infinite many solutions is ______.Log in to check the answer
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Open questionECMCQ1 markNeeds review
Consider the
matrix
It is given that
has only one real eigenvalue. Then the real eigenvalue of
isYour answerChoose one option.
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Open questionECNAT1 markNeeds review
The rank of the matrix
is __________.
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Open questionECMCQ1 markNeeds review
The rank of the matrix
isYour answerChoose one option.
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