Instrumentation Engineering
GATE IN topic:linear-algebra PYQs
Build your understanding with focused practice from past exam papers.
How to practice topic:linear-algebra
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 1–10 of 23. Imported answers require independent review unless marked reviewed.
Question 11
Open questionINMCQ1 markNeeds review
A matrix
satisfies
where
is a
identity matrix.The set of all possible eigenvalues of matrix
is ___.Your answerChoose one option.
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Open questionINMCQ1 markNeeds review
Consider a matrix
Let
and
The number of solutions to the linear system of equations
is _____.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 11
Open questionINMCQ1 markNeeds review
A
matrix
has its elements as
where
is any integer greater than 2 and
is any non-zero real number. The rank of
isYour answerChoose one option.
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Open questionINNAT1 markNeeds review
If one of the eigenvectors of the matrix
is along the direction of
, where
is any non-zero real number, then the value of
is _____ (in integer).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 19
Open questionINMCQ1 markNeeds review
A matrix
is constructed by stacking three column vectors
as
Choose the set of vectors from the following options such that
.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 26
Open questionINNAT1 markNeeds review
A
matrix
with all real elements has eigenvalues
,
, and
. The value of
is ______ (rounded off to nearest integer).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 11
Open questionINMCQ1 markNeeds review
Choose solution set
corresponding to the systems of two equations
Note:
denotes the set of real numbersYour 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 63
Open questionINNAT2 marksNeeds review
The rank of the matrix
given below is one. The ratio
is ______ (rounded off to the nearest integer).
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Open questionINMSQ1 markNeeds review
Given
, which of the following statement(s) is/are correct?Your answerSelect all correct options. You can choose more than one.
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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 49
Open questionINMSQ2 marksNeeds review
The matrix
has eigenvalues
and 7. The eigenvector(s) is/are ______Your answerSelect all correct options. You can choose more than one.
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