A=[[|gathered 1 0 0 0 0 gathered]]||2A|^3=2^21 , Z

Question

$A=[[|\begin{gathered} 1 \quad  0 \quad  0 \ 0 \quad  \alpha  \quad  \beta \ 0 \quad  \beta  \quad  \alpha \end{gathered}]]||2A{|}^{3}={2}^{21}\alpha ,\beta \in Z\alpha $

Accepted Answer

$\begin{gathered} |A|={\alpha }^{2}-{\beta }^{2} \ |2A{|}^{3}={2}^{21}\Rightarrow |A|={2}^{4} \ {\alpha }^{2}-{\beta }^{2}=16 \ (\alpha +\beta )(\alpha -\beta )=16\Rightarrow \alpha =45 \end{gathered}$

Solutions · 1