Give the correct answer and solve the given equation Let displaystyle{p}{left({x}right)}={2}+{x}{quadtext{and}quad}{q}{left({x}right)}={x}. Using the

UkusakazaL 2020-11-01 Answered
Give the correct answer and solve the given equation
Let p(x)=2+xandq(x)=x. Using the inner product  p, q=11pqdx find all polynomials r(x)=a+bxP1(R)P
(R) such that {p(x), q(x), r(x)} is an orthogonal set.
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Expert Answer

mhalmantus
Answered 2020-11-02 Author has 106 answers
Notice that
{p,q}=11(2+x)xdx=112xdx+11x2dx
=x2|11+x33|11
=(12(1)2)+(133(1)33)
=(11)+(1313)
=2/3 Thus,{p,q}0,
so the set {p(x), q(x), r(x)} cannot be orthogonal
There exist none such r(x)
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