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    Linear Algebra: Vector Spaces

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    Consider R2 with the following rules of multiplications and additions: For each x=(x1,x2), y=(y1,y2):
    x+y=(x2+y2,x1+y1) and for any scalar alpha, alpha*x=(alpha*x1, alpha*x2)

    Is it a vector space, if not demonstrate which axioms fail to hold. Also, show that Pn- the space of polynomials of order less than n is a vector space.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:49 pm ad1c9bdddf

    Solution Preview

    Here is the definition of a VECTOR SPACE:

    There is an addition '+' in V such that V,+ is a commutative group.
    Any element v in V and any r in R determine a scalar product rv in V.
    This scalar product has the following properties for any r,s in R and any v,w in V. ...

    Solution Summary

    Mulitplication and addition rules are investigated for vectors and scalars.