Show that vector p and q are orthogonal

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Reference no: EM13191171

Consider the vector space P2 of all polynomials p(t) of degree 2. For any two vector p(t),q(t) ε P2. We define the operation <p,q>=

1/ using generic vectors p(t), q(t),r(t) ε P2 is an inner product space with the defined operation by checking the validity of all four axioms defining an i.p.s

For the rest of this problem , let p(t) = t, and q(t)= t2

2/ Find the lengths

3/Show that vector p and q are orthogonal

4/ Is the set B={p,q} a basis for a vector space P2 ? Justify your anwser

5/ Find the distance between vector p and q

6/ verify the Pythagorean Theorem

7/ Verify that Triangle Inequality

8/ Consider the following subset of the vector space P2 : W= Span {p,q}

a/ Indicate why W is subspace of P2

b/ Show the vector r(t) = 0 ( the zero polynomial ) is in W by using the definition of W

c/ Find an orthonormal basis for W

Reference no: EM13191171

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