Question

Exercitiul 1 punctul c

Answer 1

B+xA=$\left[\begin{array}{ccc}0&0&1\\0&1&0\\1&0&0\end{array}\right]$+x$\left[\begin{array}{ccc}0&1&0\\1&0&1\\0&1&0\end{array}\right]$=$\left[\begin{array}{ccc}0&0&1\\0&1&0\\1&0&0\end{array}\right] +[tex] \left[\begin{array}{ccc}0&x&0\\x&0&x\\0&x&0\end{array}\right]$=$\left[\begin{array}{ccc}0&x&1\\x&1&x\\1&x&0\end{array}\right]$


det(B+xA)=1⇒ 2$x^{2}$-1=1⇒$x^{2}$=1⇒x₁,₂=±1⇒