GATE MA 2018 Paper 1 — page 19

Questions 55–57 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 19 of 22

Let

be a

matrix with real entries. If three solutions of the linear system of differential equations

are given by

then the sum of the diagonal entries of

is equal to _________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

is a solution of the differential equation

for some real numbers

and

, then

_________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be the Hilbert space of all real valued square integrable functions on

with the usual inner product. Let

be the linear functional on

defined by

where

denotes the Lebesgue measure on

. Then

_________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

2018 · Paper 1