GATE MA concept:characteristic-polynomial PYQs & Answers

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concept:characteristic-polynomial

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Questions 1–4 of 4. Imported answers require independent review unless marked reviewed.

Topic practice 4 questionsPage 1 of 1

Let

denote the characteristic polynomial of a square matrix

. Then, for which of the following invertible matrices

, the polynomial

is constant?

Your answerSelect all correct options. You can choose more than one.

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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)

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Let

and

be the linear transformation given by

. The characteristic polynomial of

Your answerChoose one option.

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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.

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GATE MA concept:characteristic-polynomial PYQs

How to practice concept:characteristic-polynomial

Question 23

Question 27

Question 19

Question 20