To calculate the relative vector of B we have to:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
The coordenates of:
[tex]p(t)= 12t^3-8t^2-12t+7[/tex], with respect to B satisfy:
[tex]C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3[/tex]
Equating coefficients of like powers of t produces the system of equation:
[tex]\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.[/tex]
After solving this system, we have to:
[tex]C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}[/tex]
And the result is:
[tex]P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right][/tex]
Learn more: brainly.com/question/16850761
