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Simple way to explain this to an undergrad?
Posted:
Jan 19, 2011 11:27 AM
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Hi,
I am wondering if anyone can give a simple way to answer the following
question in a way that is understandable to a first or second year
college student (i.e. one who has not taken a course in abstract
algebra).
Typically students are taught two the following 2 basic facts about
matrices:
Fact 1 : For A, a matrix of size mxp and B, a matrix of size rxn, the
matrix product AB is defined iff p=r.
Fact 2 : scalars can be considered as 1x1 matrices
Given these two facts, the question arises as to how we can say that
the products cA and Ac are defined (if m ne 1 and p ne 1 resp for the
matrix A described above).
One way around this is to simply define scalar multiplication (as it
is normally defined), but this still leads this nagging doubt as to
how one resolves this apparent inconsistency that exists with the
aforementioned 2 facts.
Sorry for this seemingly stupid question, but it just bugs me a bit.
Thanks,
Fran Khossa
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