finding standard matrices?

[computerages]

Hello!

My teacher gave the following problem.. I am pretty confused as to where to start from... can anyone help?

Find the standard matrices for the derivative and integral operators for polynomials up to degree 4. Use vectors of length 5 to represent the polynomials

Thanks in advance! any help would be greatly appreciated!

[Vid]

Think about what differentiation and integration do to a polynomial algebraically without thinking in terms of limits or difference quotients.