Question:
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.