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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

given a linear transformation F so that this is known

\(\displaystyle \left\{

\begin{aligned}

\phantom{1}F(1,0,0)=(1,2,3) \\

F(1,1,0)=(0,0,1)\\

F(1,1,1)=(12,3,4)\\

\end{aligned}

\right.\)

Decide F

progress:

\(\displaystyle F(e_1)=(1,2,3)\)

\(\displaystyle F(e_2)=F(e_1)+F(e_2)-F(e_1)=(0,0,1)-(1,2,3)=(-1,-2,-2)\)

\(\displaystyle F(e_3)=F(e_1)+F(e_2)+F(e_3)-(F(e_1)+F(e_2))= (12,3,4)-(-1,-2,-2)=(13,5,6)\)

My \(\displaystyle f(e_3)\) is wrong acording to facit and I don't understand

Regards,

\(\displaystyle |\pi\rangle\)