Răspuns
Explicație pas cu pas:
[tex]A = \left[\begin{array}{ccc}x-4&1\\1&x-4\end{array}\right] \\\\a) det(A) =0 =>(x-2)^2 - 1 = 0 => x^2-8x+16-1 = x^2-8x+15 = 0\\\Delta = 8^2-4*1*15 = 64 - 60 = 4\\\\x_1 = \frac{8+\sqrt{4}}{2} = 5\\ x_2 = \frac{8-\sqrt{4}}{2} = 3\\\\\\b) A^2 = A*A = \left[\begin{array}{ccc}-2&1\\1&-2\end{array}\right]*\left[\begin{array}{ccc}-2&1\\1&-2\end{array}\right] =\\ \\\left[\begin{array}{ccc}5&-4\\-4&5\end{array}\right][/tex]
