If On denotes the vector space of all polynomial of degree ≤ n , give two linearly independent elements of P4/PE.
A Polynomial of degree n is a function of the form-
where are real numbes called coefficient and n is called the degree of the polynomial.
Polynomial can be represented by the vector of their coefficient in vector space as-
Linear operation are defined on the piolynomial of same degree i.e n
Consider two polynomial-
Then The addition operation is given by-
Here polynomial p(x) and (g(x) are linearly independent since niether the value of P(x) depends upon Q
nor G(x) value depens upon P.
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