We can define a one-to-one correspondence between the elements of Pn and Rn by p(x) = a1 + a2x + a3x2 + … + anxn-1   (a1, …, an)T = a Show that if p  a and q  b, then (a) αp  αa for any scalarα. (b) p + q  a + b [In general, two vector spaces are said to be isomorphic if their elements can be put into a one-to-one correspondence that is preserved under scalar multiplication and addition as in (a) and (b).]

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