$${\cal B}=\{ t^3, t^3+t^2, t^3+t^2+t, t^3+t^2+t+1\}$$

...is a basis for the space of all polynomials of degree three or less.

$$r(t)=1-t+t^2$$

$$\vec x =\left [\matrix { a\cr b \cr c \cr d }\right ]$$

...is the coordinate vector of $r(t)$ relative to this basis. Find the components of $\vec x$.