Question

iv. 4.
True-False Questions:
Q15. A linearly independent set can contain a linearly dependent subset.
Q.16. If a set of vectors is linearly dependent, then we can add vectors to the
set and make it linearly independent.
Q.17. The set of all polynomials p of degree at most 7 s.t. p(7)=0 is a vector
space.
Q.18. The set of all vectors x=(x,x) such that x, 20 and x, 20 is a subspace of
R.
Q.19. Every subspace in a vector space V is the span of some vectors in V.
Q.20. If H is a linearly independent set of vectors in some vector space, then H
is a basis for the span of HI

Answer 1

Answer:

1. false
2. false
3. true
4. false
5. tre

Answer 2

Answer:

15.False

16.False

17.True

18.False

19.True

Step-by-step explanation:

• No,this is completely wrong statement a linearly independent set can never contain a linearly dependent subset.
• No, we cannot make dependent vectors independent by adding.
• Yes set of all polynomials is a vector space.
• No, this is not correct statement as it will be set of 20 natural numbers.
• Yes if H is linearly independent then we can calculate HI with the help of H.

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