$$\begin{equation}
A=\begin{pmatrix}
\frac{1}{2}& \frac{1}{6} & \frac{1}{10}\\
0& \frac{1}{2} & \frac{3}{10}\\
\frac{1}{2} & \frac{1}{3} & \frac{3}{5}\\
\end{pmatrix}
\end{equation}$$
Bepaal $A^3$.
$$\begin{equation*}
A^3=
\begin{pmatrix}
\frac{3}{10}& \frac{1}{5} & \frac{4}{25}\\
\frac{3}{20}& \frac{7}{20} & \frac{33}{100}\\
\frac{11}{20} & \frac{9}{20} & \frac{51}{100}\\
\end{pmatrix}
\end{equation*}$$
$$\begin{equation*}
A^3=
\begin{pmatrix}
\frac{26}{125}& \frac{101}{500} & \frac{489}{2500}\\
\frac{279}{1000}& \frac{301}{1000} & \frac{1539}{5000}\\
\frac{513}{1000} & \frac{497}{1000} & \frac{2483}{5000}\\
\end{pmatrix}
\end{equation*}$$
$$\begin{equation*}
A^3=
\begin{pmatrix}
\frac{1}{4}& \frac{1}{36} & \frac{1}{100}\\
0& \frac{7}{20} & \frac{9}{100}\\
\frac{1}{4} & \frac{1}{9} & \frac{9}{25}\\
\end{pmatrix}
\end{equation*}$$
$$\begin{equation*}
A^3=\begin{pmatrix}
\frac{23}{100}& \frac{61}{300} & \frac{93}{500}\\
\frac{24}{100}& \frac{31}{100} & \frac{159}{500}\\
\frac{53}{100} & \frac{73}{150} & \frac{62}{125}\\
\end{pmatrix}
\end{equation*}$$
Correct:
$$\begin{equation}
A^3=A\cdot A \cdot A=
\begin{pmatrix}
\frac{23}{100}& \frac{61}{300} & \frac{93}{500}\\
\frac{24}{100}& \frac{31}{100} & \frac{159}{500}\\
\frac{53}{100} & \frac{73}{150} & \frac{62}{125}\\
\end{pmatrix}
\end{equation}$$
Ga door
Fout: Dit is $A^2$.
Probeer de opgave nogmaals.
Fout: Dit is $A^4$.
Probeer de opgave nogmaals.
Fout: Een matrix-vermenigvuldiging gaat niet elementsgewijs.
Zie Extra uitleg: matrix-matrix vermenigvuldigen.