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## Homework Statement

Definition of spanning set:

Let be vectors in the vector space . The

**set**of all linear combination of the vectors is a subspace ( say ) of . The subspace is called the space spanned by the vectors The

**set**is called a

**spanning set**of .

Definition of linear independence:

Suppose that is a vector space. The set of vectors from is

**linearly**dependent if there is a relation of

**linear**dependence on that is not trivial. In the case where the only relation of

**linear**dependence on is the trivial one, then is a

**linearly independent**set of vectors.

Definition of basis of vector space:

1. It spans the space.

2. Its vectors are independent.

3. The number of vectors in the basis is equal to the dimension of the space.

True or false? Given reason

1. A set of 5 Vectors in R5 must be a basis for R5

2. A set of 6 Vectors in R5 cannot be a basis for R5

3. A set of 7 vectors in R5 must be a spanning set for R5

4. A set of 6 polynomials in R5 must be a basis for R5

5. A set of 6 polynomials in R5 may be a basis for R5

Anyone help me to explain these question.. I want to know the reason cz it's confused me a lot and i always get mess about these kind of question

appericated it!

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