A5.pdf - Math 235 Assignment 5 1 Let S = Spancfw_1 x2 be a...

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Math 235Assignment 51.LetS= Span{1 +x2}be a subspace ofP2(R).Find a basis forSunder the innerproducthp, qi=p(-1)q(-1) +p(0)q(0) +p(1)q(1)2.LetS= Span1-11,101be a subspace ofR3and let~w=112.a) Find an orthonormal basis forS.b) Find projS~w.c) Find a basis forS.3.Suppose thatP2(R) has inner producth,ithat satisfies the following:h1,1i= 2,h1, xi= 2,1, x2=-2hx, xi= 4,x, x2=-2,x2, x2= 3LetB={2, x, x2}. Apply the Gram-Schmidt procedure toB(in this order)to find an orthonormal basisCofP2(R).4.Define the inner producth~x, ~yi= 2x1y1+ 2x2y2+x3y3on

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