Mathematics: Find the matrix a of the linear transformation t(f(t))= 4f (t)+6f(t) from p2 t0 p2 with respect to the standard basis of p2 {1,t,t^2} you don t need to answer the full question i have the answer just tips on where to start and on what to do would be nice.

The answer is 2a^3-3a^2-45a+50...

Find the matrix a of the linear transformation

Ответ:

adamske0

11.01.2022

Mathematics

The required matrix is

$A=\left[\begin{array}{ccc}6&4&0\\0&6&8\\0&0&6\end{array}\right] .$

Step-by-step explanation: The given linear transformation is

T(f(t)) = 4f'(t) + 6f(t).

We are to find the matrix A of T from P² to P² with respect to the standard basis P² = {1, t, t²}.

We have

$T(1)=4\times\dfrac{d}{dt}1+6\times1=0+6=6\times 1+0\times t+0\times t^2,\\\\T(t)=4\times\dfrac{d}{dt}t+6\times t=4+6t=4\times1+6\times t+0\times t^2,\\\\T(t^2)=4\times\dfrac{d}{dt}t^2+6\timest^2=8t+6t^2=0\times 1+8\times t+6\times t^2.$

Therefore, the matrix A is given by

$A=\left[\begin{array}{ccc}6&4&0\\0&6&8\\0&0&6\end{array}\right] .$

Thus, the required matrix is

$A=\left[\begin{array}{ccc}6&4&0\\0&6&8\\0&0&6\end{array}\right] .$

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Find the matrix a of the linear transformation t(f(t))= 4f'(t)+6f(t) from p2 t0 p2 with respect to the standard basis of p2 {1,t,t^2}

you don't need to answer the full question i have the answer just tips on where to start and on what to do would be nice.

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Find the matrix a of the linear transformation t(f(t))= 4f'(t)+6f(t) from p2 t0 p2 with respect to the standard basis of p2 {1,t,t^2} you don't need to answer the full question i have the answer just tips on where to start and on what to do would be nice.

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Find the matrix a of the linear transformation t(f(t))= 4f'(t)+6f(t) from p2 t0 p2 with respect to the standard basis of p2 {1,t,t^2}

you don't need to answer the full question i have the answer just tips on where to start and on what to do would be nice.