GATE MA discipline:mathematics-and-statistics PYQs & Answers — Page 58

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Questions 571–580 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 58 of 65

Consider

with the usual inner product. If

is the distance from

to the subspace

, then

_________.

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Consider the matrix

with

, where

is the

identity matrix and

is the transpose of

. If

and

are two distinct eigenvalues of

, then

_________.

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Let

for

and let

be the circle

, where

varies from 0 to

. Then

_________.

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Let

be the surface of the solid

Let

denote the unit outer normal to

and let

Then the surface integral

equals _________.

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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 _________.

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is a solution of the differential equation

for some real numbers

and

, then

_________.

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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

_________.

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Let

be an orthonormal set in a Hilbert space

and let

be such that

. Consider the set

Then the maximum possible number of elements in

is _________.

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interpolates the points

in the table

then

_________.

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for

, then

_________.

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GATE MA discipline:mathematics-and-statistics PYQs

Question 41

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Question 50