Mathematics
GATE MA concept:minimal-polynomial PYQs
Build your understanding with focused practice from past exam papers.
How to practice concept:minimal-polynomial
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 27
Open questionMANAT1 markNeeds review
Let
be a
matrix with entries in
and having the characteristic polynomial
Let
, where
is the
identity matrix. If
is the minimal polynomial of
, then
is equal to _____ (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 22
Open questionMAMCQ1 markNeeds review
Let
be a linear transformation and the null space of
be the subspace of
given by
If
, where
is the identity map on
, then the minimal polynomial of
isYour 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 60
Open questionMANAT2 marksNeeds review
Let
be a
real matrix such that
If
is the degree of the minimal polynomial of
, then
equals __________.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 20
Open questionMANAT1 markNeeds review
If the characteristic polynomial and minimal polynomial of a square matrix
are
and
, respectively, then the rank of the matrix
is _____, where
is the identity matrix of appropriate order.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 27
Open questionMAMCQ2 marksNeeds review
Given two
matrices
and
with entries in
, consider the following statements:
(P): If
and
have the same minimal polynomial, then
is similar to
.
(Q): If
has
distinct eigenvalues, then there exists
such that
are linearly independent.
Which of the above statements hold TRUE?Your answerChoose one option.
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