GATE MA 2020 Paper 1 — page 8

Questions 22–24 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 8 of 22

Suppose that

is a

matrix with real entries and

. Then

Your answerChoose one option.

every eigenvalue of

is real if

is necessarily a polynomial in

of degree 4 if

is invertible

is not invertible if

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Let

denote the space of all real-valued continuous functions on

equipped with the supremum norm

. Let

be such that

For

, let

. If

, then

Your answerChoose one option.

the closure of

is compact

is closed and bounded

is bounded but not totally bounded

is compact

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Let

be a function such that the solution of the initial value problem

is given by

for all bounded continuous functions

. Then the value of

is ________

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2020 · Paper 1