i t is not so easy to do any meaningful computation in them But as we have seen if we have a basis f or an arbitrary finite dimensional vector space V then the coordinate mapping ID: 578494
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Arbitrary vector spaces are so …it is not so easy to do any meaningful computa-tion in them. But, as we have seen, if we have a basis for an arbitrary finite dimensional vector space V, then the coordinate mappingestablishes an isomorphism (one-to-one, onto linear transformation) between V and
CHANGE OF BASESSlide2
Note that Slide3
The following picture helps us visualize the situation:Slide4
Let’s look at another figure.Note the textbook’s notation, plus the fact thatall arrows are isomorphisms. Also note thatSlide5
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Solution. FromSlide10Slide11
For ease we copy the four vectorsSlide12
Both are non homogeneous systems of two equa-tions in two unknowns, and both require row reducing the matrix to the identity