Question

what is the dimensional of the vector space of all real polynomials with degree less than or equal to n
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Answer 1

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Answer 2

SOLUTION

TO DETERMINE

The dimension of the vector space of all real polynomials with degree less than or equal to n

EVALUATION

CONCEPT TO BE IMPLEMENTED

Basis

Let V be a vector space over a field F. A set S of vectors in V is said to be basis of V if

• S is linearly independent

• S generates V

EVALUATION

Here the given vector space is the vector space of all real polynomials with degree less than or equal to n

Now the set of polynomials

$\sf{ \{ \: 1,x, {x}^{2} , {x}^{3} ,..., {x}^{n} \: \} }$

is the basis

Since above set contains ( n + 1 ) elements

So required dimension = n + 1

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