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Define the Duality Principal and Multiplying Matrices of Differing Size

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1) Please explain in your own words the duality principle.
2) The biggest problem I have with matrices is the multiplication. I get them right but I believe the confusion comes from the way it is set up. To be more clear the way it is set up as far as the rows and columns. If it is a 3 x 2 times a 4 x 3 it can become somewhat confusing. This is for multiplication only. Do you have any suggestions for me that might help?

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Please see the attached file for the complete solution.

1) Please explain in your own words the duality principle.
The duality principle states that for any projective result established using points and hyperplanes, a symmetrical result holds in which the roles of hyperplanes and points are interchanged: points become planes, the points in a plane become the planes through a point, etc. For example, in the projective plane, any two distinct points define a line (i.e. a hyperplane in 2D). Dually, any two distinct lines define a point ...

Solution Summary

Duality principal is defined and the multiplying of matrices of different sizes is discussed. The solution is detailed and well presented.

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