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## Homework Statement

For each of the following pairs of vectors, define an explicit isomorphism to establish that the spaces are isomorphic. Prove that your map is an isomorphism.

a)P3 and R4

b)P5 and M(2,3)

## Homework Equations

None

## The Attempt at a Solution

a)I know that P3 and R4 are isomorphic because if the entries in a given polynomial in P3 are written out in a single row (or column), the result is a vector in R4 because we have 4 coefficients in a polynomial of highest degree 3

b)I also know that P5 and M(2,3) are isomorphic because if the entries in a given 2 by 3 matrix are written out in a single row (or column), the result is a vector in R6 , and, likewise, if the entries in a given polynomial in P5 are written out in a single row (or column), the result is a vector in R6 because we have 6 coefficients in a polynomial of highest degree 5

However, I'm not sure exactly sure how the question wants me to write my answers. Could you help me refine my answer so that I am answering what the question wants me to?