Matemática, perguntado por feh29, 1 ano atrás

Alguém me ajuda por favorrrrrr!

Anexos:

Soluções para a tarefa

Respondido por matheushenrique66
0
são os dois dois números complexos conjugados
Respondido por Verkylen
1
A=\left(\begin{array}{aaa}2&1\\4&-2\end{array}\right)\qquad\qquad\qquad{I}=\left(\begin{array}{aaa}1&0\\0&1\end{array}\right)\\\\\\\\\det(A-kI)=0\\\\\\\left|\begin{array}{aaa}2&1\\4&-2\end{array}\right|-k\left|\begin{array}{aaa}1&0\\0&1\end{array}\right|=0\\\\\\\left|\begin{array}{aaa}2&1\\4&-2\end{array}\right|-\left|\begin{array}{aaa}k&0\\0&k\end{array}\right|=0\\\\\\\left|\begin{array}{aaa}2-k&1\\4&-2-k\end{array}\right|=0\\\\\\(2-k)(-2-k)-(4)(1)=0\\\\(-4-2k+2k+k^2)-(4)=0\\\\-4+k^2-4=0\\\\k^2-8=0\\\\k^2=8\\\\k=\pm\sqrt{8}\\\\\boxed{\boxed{k=\pm2\sqrt{2}}}\\\\\\\\\text{Alternativa c).}
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