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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 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 ...

    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.