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Find
||u||, ||v||, and d(u,v)
for given inner product defined on R^n:
1) u=(3,7), v=(5,-12),<u,v>=u.v (answeris: 5 -- 13, -- 2 *(65)^0.5 )
2) u=(-4,3), v=(0,5), <u,v>=3*u1*v1 +2*u2*v2 (answeris: (57)^0.5 -- 5 -- 2 *(13)^0.5)
please show me the solutin in details.
and how to find the angle for inner product ??
Using the inner product <u,v>=2u1 v1 +u2 v2 in R2 and the G.S-Process, one can transform {(2,-1),(-2,10)} into an orthonormal basis . Explain why this result is not an orthonormal basis when the euclidean inner product on R2 is used.
Consider C[รขยย1, 1] with inner product <f,g> = integral -1 to 1 f(x)g(x) dx. Let f(x) = x and g(x) = x2-x
a) Find <f,g>.
b) Find llfll
c) By Gram-Schmidt process, find an orthogonal basis for the space W = span{f, g} .
d) Find the least squares approximation of h(x) = 1 in W.