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## Homework Statement

1) In a vector space V of all real polynomials of third degree or less find basis B such that for arbitrary polynomial p \in V the following applies:

[p]_B = \begin{pmatrix} p'(0)\\p'(1)\\p(0)\\p(1)\end{pmatrix} where p' is the derivative of the polynomial p.

## Homework Equations

## The Attempt at a Solution

Would somebody be so kind and pointed me in a direction how to solve this? I have missed couple last lectures and I can´t seem to find this specifit type of problem anywhere.. Thanks:)

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