Show that the functions x and x^2 are orthogonal in P5 with inner product defined by ( <p,q>=sum from i=1 to n of p(xi)*q*(xi) ) where xi=(i-3)/2 for i=1,...,5.
Show that ||X||1=sum i=1 to n of the absolute value of Xi.
Show that ||x||infinity= max (1<=i<=n) of the absolute value of Xi.
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Vector relations are proven given an inner product. The solution is detailed and well presented.