Question

Am incercat cu teorema Hamilton Cayley dar nu am gasit o formula pt A
Am nevoie doar de cateva indicatii multumesc

Answer 1

Am atașat rezolvarea mai jos!

Answer 2

$A^2-\lambda A+\lambda^2I_2 = O_2\\ \\ A^2 = \lambda A-\lambda^2I_2 \\ A^2 = \lambda(A-\lambda I_2)\\ A^4 = \lambda ^2(A^2-2A\lambda +\lambda^2I_2)\\ A^4 = \lambda^2(A^2-\lambda A +\lambda^2I_2 -\lambda A) \\ A^4 = \lambda^2(O_3-\lambda A) \\ A^4 = \lambda^2(-\lambda A) \\ A^4 = -\lambda^3A\\ A^3 = -\lambda^3I_2 \\ \\ A^{2018} = (A^3)^{672}\cdot A^2 = (\lambda I_2)^{3\cdot 672}\cdot A^2 = (\lambda I_{2})^{2016}A^2\\ \\ \Rightarrow A^{2018} = \lambda^{2016}A^2$