Title: H5P proov1

Ilma pealkirjata Text

Sümmetriline rühm \(S_{3}\) on kolmeelemendilise hulga \(\left\{ 1,2,3\right\} \) substitutsioonide \(\sigma =\left(
\begin{array}{ccc}
1 & 2 & 3 \\
\sigma \left( 1\right)  & \sigma \left( 2\right)  & \sigma \left( 3\right)
\end{array}
\right) \) rühm, st.  \(
S_{3}=\left\{ e,a,b,c,d,f\right\} ,\) kus
\begin{align*}
&e=\left(
\begin{array}{lll}
1 & 2 & 3 \\
1 & 2 & 3
\end{array}
\right) ,\text{  }a=\left(
\begin{array}{lll}
1 & 2 & 3 \\
2 & 3 & 1
\end{array}
\right) ,\text{  }b=\left(
\begin{array}{lll}
1 & 2 & 3 \\
3 & 1 & 2
\end{array}%
\right) ,\\&c=\left(
\begin{array}{lll}
1 & 2 & 3 \\
1 & 3 & 2%
\end{array}%
\right) ,\text{ }d=\left(
\begin{array}{lll}
1 & 2 & 3 \\
2 & 1 & 3%
\end{array}%
\right) ,\text{ }f=\left(
\begin{array}{lll}
1 & 2 & 3 \\
3 & 2 & 1%
\end{array}%
\right) .
\end{align*}

Rühma \(S_{3}\) elementide kor-

rutamine on defineeritud:

\(\left( \sigma \circ \rho
\right) \left( x\right) =\sigma \left( \rho \left( x\right) \right) .\)

Ülesanne.

Leida \(c\circ f\) ja \(f\circ c\).

Ilma pealkirjata Drag the Words

ANSWER: Drag and drop!

Q: [...]
A: 2 3 1
Also offered: 1 2 3; 1 3 2; 2 1 3; 3 1 2; 3 2 1

\(\left( c\circ f\right) \left( 1\right) =c\left( f\left( 1\right) \right)
=c(3)=2\)

\(\left( c\circ f\right) \left( 2\right) =c\left( f\left( 2\right) \right)
=c(2)=3\)

\(\left( c\circ f\right) \left( 3\right) =c\left( f\left( 3\right) \right)
=c(1)=1.\)

Ilma pealkirjata Drag the Words

ANSWER: Drag and drop!

Q: [...]
A: 3 1 2
Also offered: 1 2 3; 1 3 2; 2 1 3; 3 2 1; 2 3 1

\(\left( f\circ c\right) \left( 1\right) =f\left( c\left( 1\right) \right)
=f(1)=3\)

\(\left( f\circ c\right) \left( 2\right) =f\left( c\left( 2\right) \right)
=f(3)=1\)

\(\left( f\circ c\right) \left( 3\right) =f\left( c\left( 3\right) \right)
=f(2)=2.\)

Ilma pealkirjata Text

\(c\circ f=\left(
\begin{array}{lll}
1 & 2 & 3 \\
  &  & %
\end{array}%
\right) \)

Ilma pealkirjata Text

\(f\circ c=\left(
\begin{array}{lll}
1 & 2 & 3 \\
  &  & %
\end{array}%
\right) \)