The set $B=\set{\vect{v}_1,\,\vect{v}_2,\,\vect{v}_3,\,\vect{v}_4}$ is a basis of the vector space $P_3$, polynomials with degree 3 or less. Therefore $\vectrepname{B}$ is a linear transformation, according to Theorem VRLT. Find a “formula” for $\vectrepname{B}$. In other words, find an expression for $\vectrep{B}{a+bx+cx^2+dx^3}$. \begin{align*} \vect{v}_1&=1 - 5x - 22x^2 + 3x^3 & \vect{v}_2&=-2 + 11x + 49x^2 - 8x^3\\ \vect{v}_3&=-1 + 7x + 33x^2 - 8x^3 & \vect{v}_4&=-1 + 4x + 16x^2 + x^3 \end{align*}