Výsledky cvičení.

1.
a) $\lambda_1 = -4, \lambda_2 = 1$, ${\bf v^{(\it 1)}} = (0, 1)^T$, ${\bf v^{(\it 2)}} = (1, 0)^T$
b) $\lambda_1 = -5, \lambda_2 = 5$, ${\bf v^{(\it 1)}} = (-1, 2)^T$, ${\bf v^{(\it 2)}} = (2, 1)^T$
c) $\lambda_1 = 0, \lambda_2 = 0$, ${\bf v^{(\it 1)}} = (0, 1)^T$, ${\bf v^{(\it 2)}} = (1, 0)^T$
d) $\lambda_1 = -1, \lambda_2 = 1$, ${\bf v^{(\it 1)}} = (-1, 1)^T$, ${\bf v^{(\it 2)}} = (1, 1)^T$
e) $\lambda_1 = (6-4\sqrt 14)/2, \lambda_2 = (6+4\sqrt 14)/2$, ${\bf v^{(\it 1)}} = ((-2(-2+\sqrt 14))/5, 1)^T$, ${\bf v^{(\it 2)}} = ((2(2+\sqrt 14))/5, 1)^T$
f) $\lambda_1 = (-3-\sqrt 17)/2, \lambda_2 = (-3+\sqrt 17)/2$, ${\bf v^{(\it 1)}} = ((3-\sqrt 17)/2, 1)^T$, ${\bf v^{(\it 2)}} = ((3+\sqrt 17)/2, 1)^T$
g) $\lambda_1 = -1, \lambda_2 = 7$, ${\bf v^{(\it 1)}} = (1, 1)^T$, ${\bf v^{(\it 2)}} = (-1, 1)^T$
h) $\lambda_1 = (1-\sqrt 229)/2, \lambda_2 = (1+\sqrt 229)/2$, ${\bf v^{(\it 1)}} = ((11-\sqrt 229)/6, 1)^T$, ${\bf v^{(\it 2)}} = ((11+\sqrt 229)/6, 1)^T$
i) $\lambda_1 = -1 -i, \lambda_2 = -1+i, \lambda_3 = 0$, ${\bf v^{(\it 3)}} = (0, 0, 1)^T$
j) $\lambda_1 = -5, \lambda_2 = 3, \lambda_3 =3$, ${\bf v^{(\it 1)}} = (-1, -2, 1)^T$, ${\bf v^{(\it 2)}} = (3, 0, 1)^T$, ${\bf v^{(\it 3)}} = (-2, 1, 0)^T$
k) $\lambda_1 = 2, \lambda_2 = 6, \lambda_3 =8$, ${\bf v^{(\it 1)}} = (1, -2, 1)^T$, ${\bf v^{(\it 2)}} = (1, 0, 0)^T$, ${\bf v^{(\it 3)}} = (5, 1, 0)^T$
l) $\lambda_1 = 0, \lambda_2 = 0, \lambda_3 =8$, ${\bf v^{(\it 1)}} = (3, 0, 1)^T$, ${\bf v^{(\it 2)}} = (-2, 1, 0)^T$, ${\bf v^{(\it 3)}} = (1, 2, -1)^T$
m) $\lambda_1 = 2, \lambda_2 = 2, \lambda_3 =9$, ${\bf v^{(\it 1)}} = (-1, 0, 2)^T$, ${\bf v^{(\it 2)}} = (0, 1, 0)^T$, ${\bf v^{(\it 3)}} = (3, 1, 1)^T$
n) $\lambda_1 = -10, \lambda_2 = -4, \lambda_3 =0$, ${\bf v^{(\it 1)}} = (1, -1, 1)^T$, ${\bf v^{(\it 2)}} = (0, 1, 0)^T$, ${\bf v^{(\it 3)}} = (3, 0, 1)^T$.