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$${\cal B}=\{ t^3, t^3+t^2, t^3+t^2+t, t^3+t^2+t+1\}$$ a basis for the space of all polynomials of degree three or less.


$$\vec x =\left [\matrix { a\cr b \cr c \cr d }\right ]$$ the coordinate vector of $r(t)$ relative to this basis. Find the components of $\vec x$.

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