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Linear Algebra: Vector Spaces

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.

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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.