Find (a) <p,q>, (b) ||p||, (c) ||q||, and (d) d(p,q) for the polynomials in P_2 using the inner product <p,q>=a_0b_0+a_1b_1+a_2b_2.

waigaK 2021-09-04 Answered

Find (a) , (b) ||p||, (c) ||q||, and (d) d(p,q) for the polynomials in P2 using the inner product <p,qa0b0+a1b1+a2b2.
p(x)=13x+x2,q(x)=x+2x2

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Expert Answer

coffentw
Answered 2021-09-05 Author has 103 answers

We have given that.
p(x)=13x+x2, q(x)=x+2x2
a) The inner product of the polynomials will be:
p(x)=13x+x2,q(x)=x+2x2
<p,q1×0+(3)(1)+1(2)
<p,q3+2
<p,q5
b) ||p||=12+(3)2+12
||p||=1+9+1
||p||=11
c) ||q||=(1)2+22
||q||=1+4
||q||=5
d) d(p,q)=||pq||
d(p,q)=||13x+x2(x+2x2)||
d(p,q)=||13x+x2+x2x2||
d(p,q)=||12xx2||
d(p,q)=12+(2)2+(1)2
d(p,q)=1+4+1
d(p,q)=6

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