Bestimme den Wert des Parameters a

Bestimme den Wert des Parameters a

$\det\left( \begin{array}{rrrr}a-1 & -2 \\-\frac{2}{5} & 4 \\\end{array}\right) =\dfrac{6}{5}$

$\begin{array}{|rcll|} \hline \det\left( \begin{array}{rrrr}a-1 & -2 \\-\frac{2}{5} & 4 \\\end{array}\right) &=& \dfrac{6}{5} \\ (a-1)*4- \left(-\dfrac{2}{5} \right)(-2) &=& \dfrac{6}{5} \\ 4a-4 - \left(\dfrac{2}{5} \right)*2 &=& \dfrac{6}{5} \\ 4a-4 - \dfrac{4}{5} &=& \dfrac{6}{5} \quad |\quad + \dfrac{4}{5} \\ 4a-4 &=& \dfrac{6}{5} + \dfrac{4}{5} \\ 4a-4 &=& \dfrac{6+4}{5} \\ 4a-4 &=& \dfrac{10}{5} \\ 4a-4 &=& 2 \quad | \quad +4 \\ 4a &=& 6 \quad | \quad :4 \\ a &=& \dfrac{6}{4} \\ \mathbf{ a } &=& \mathbf{\dfrac{3}{2}} \\ \hline \end{array}$