# Vector Geometry, Cross Products and Real Inner Products: Moorean 3-Space

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Please see the attached file for full problem description.

1. Demonstrate (check the properties) that the following function is an inner product in R^3. (Call R^3 with this inner product Moorean 3-space). Let u=(u_1,u_2,u_3) and v=(v_1,v_2,v_3). Then

<u, v> = uAv^T, where A=[ 2 0 0 ]

[ 0 1 0 ]

[ 0 0 2 ]. Show work.

Help: [ 2 0 0 ]

[ 0 1 0 ] : is a 3 x 3 matrix.

[ 0 0 2 ].

https://brainmass.com/math/vector-calculus/moorean-space-12708

#### Solution Summary

An inner product is found to b in R^3. The solution is detailed and well presented.

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