Answered: (a) (b) (c) HOD {··]} RE The set… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 66E

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Question

The options shown apply to all

(a)
(b)
(c)
2
000
-2 -3
5
2
2
{[1-6]-[]}
0 2
0
0
2
2
4
9
(0680)
3
5
11
13
The set mentioned in (a)
The set mentioned in (b)
The set mentioned in (c)
7
14
21
28
[Choose]
[Choose]
is linearly independent
is linearly dependent
spans a vector space of dimension 5
[Choose]

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None of théšé M={ (3,6),(6, 12 ), (1,2) ) The set of all polynomials of degree 4 under the standard addition and scalar multiplication operations is not a vector space because O We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)#Q(x)-P(x) O We can find a polynomial P(x) for which 1-P(x)#P(x) O We can find a polynomial P(x) such that (c+d)P(x)#cP(x)+dP(x). O It is not closed under addition.
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The set of all polynomials of degree 6 under the standard addition and scalar multiplication operations is not a vector space because" We can find a polynomial P(x) for which 1-P(x)=P(x) We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)=Q(x)•P(x) It is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)zcP(x)+dP(x).

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