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.
1 answer:
To calculate the relative vector of B we have to:
![P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]](https://tex.z-dn.net/?f=P_B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C3%5C%5C-2%5C%5C3%2F2%5Cend%7Barray%7D%5Cright%5D)
The coordenates of:
, with respect to B satisfy:

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

After solving this system, we have to:

And the result is:
![P_B=\left[\begin{array}{ccc}3\\3\\-2\\3/2\end{array}\right]](https://tex.z-dn.net/?f=P_B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C3%5C%5C-2%5C%5C3%2F2%5Cend%7Barray%7D%5Cright%5D)
Learn more: brainly.com/question/16850761
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