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Stels [109]
2 years ago
13

Let B be the basis of P3 consisting of the Hermite polynomials in Exercise 21, and let p.t / D 7 ! 12t ! 8t 2 C 12t 3. Find the

coordinate vector of p relative to B.
Mathematics
1 answer:
Anastasy [175]2 years ago
4 0

To calculate the relative vector of B we have to:

P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]

The coordenates of:

p(t)= 12t^3-8t^2-12t+7, with respect to B satisfy:

C_1(1)+C_2(2t)+C_3(-2+4t^2)+C_4(-12t+8t^3)= 7-12t-8t^2+12t^3

Equating coefficients of like powers of t produces the system of equation:

\left \{ {C_1-2C_3=7} \atop {2C_2-12C_4=-12} \right. \\\left \{ {{4C_3=-8} \atop {8C_4=12}} \right.

After solving this system, we have to:

C_1=3\\C_2= 3\\C_3= -2\\C_4= \frac{3}{2}

And the result is:

P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]

Learn more: brainly.com/question/16850761

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