- #1

karush

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MHB

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We define the application $T:P_2\rightarrow P_2$ by

$$T(p)=(x^2+1)p''(x)-xp'(x)+2p'(x)$$

1. Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ in the standard basis $\alpha=(x^2,x,1)$

2 Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ where $\beta=\{x^2+x+1,x+1,1\}$

would this be

$\left[\begin{array}{c}1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right]$

$$T(p)=(x^2+1)p''(x)-xp'(x)+2p'(x)$$

1. Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ in the standard basis $\alpha=(x^2,x,1)$

2 Give the matrix $\displaystyle\left[T\right]_\infty^\infty$ where $\beta=\{x^2+x+1,x+1,1\}$

would this be

$\left[\begin{array}{c}1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right]$

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