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To find inner product in vector spaces

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Find each of the following for the given inner product defined in R^2

a) d(u,v)
b) < u,v >

< u,v >=3u(subscript 1)v(subscript 1) + u(subscript 2)v(subscript 2)
where u=(-4,9) and v=(0,4)

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Solution Summary

This problem explains how to find inner product of two vecotrs and also distance between them.There can be different formulas for defining an inner product of two vectors;here a particular formula has been used.

Solution Preview

According to the given formula for <u,v> one has <u,v> = 3 (-4)(0) + (9)(4)= 36. As for d(u,v) it is given by positive squre root of (u(subscript1) - (v(subscript 1))^2 +(u(subscript2) - (v(subscript2) ^2. Thus in the present case,one has d(u,v) = Positive ...

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