Easy# Span of a Set of Polynomials

LINALG-WZ1PSX

Let:

$$S=\{ t^2-2t, t+3, t^3-t^2\}$$

$S$ is a set of vectors in the vector space of polynomials of degree $4$ or less with real coefficients. Suppose that:

$$p(t)=at^4+bt^3+t+1$$

...is an element in the span of $S$. Find the values of $a$ and $b$.