Please do and explain how to do number 20. 1 17-18, find llulandd(u,v) relative

Question

Please do and explain how to do number 20.

1 17-18, find llulandd(u,v) relative to the weighted Euclidean inner product(mv)=2"M+3alyon R 17. u-(-3, 2) and v = (1,7 18, u (-1, 2) and v (2,5) n Exercises 2 . ) In Exercises 19-20, find Ipl and d(p, q) relative to the standard inner product on P 19, p=2 + x + 3x-, q=4-7x2 In Exercises 21-22, find Ull and d(U, V) relative to the stan- dard inner product on M22. 3 -2 21. U 4 6 -35, In Exercises 23-24, let he p=x+x3 and q 1+x2 Find lIpl and d(p. q) relative to the evaluation inner product on Ps at the stated sample points. in Exercises 2. 26, find Ilull and dou.) for the vectors u = (-1, 2) and y (2.5) relative to the inner product on R, generated by the matrix A 25. A P: of

Explanation / Answer

20.

Given: p= x2+2x-5 ; q= -4x2+2x+3

Solution:

||p|| = [(1)2+(2)2+(-5)2]1/2

= [30]1/2   = 5.48

Hence ||p|| = 5.48

d(p,q)= ||p-q||

p-q = x2+2x-5 -(-4x2+2x+3) = 5x2 -8

Hence

||p-q|| = [(5)2+(-8)2]1/2 = (89)1/2 = 9.44

Hence d(p,q)= 9.44

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