Question

Se consideră matricele
Ajutor va rog

Answer 1

Răspuns:

aceasta este rezolvarea

Answer 2

Explicație pas cu pas:

a) det(A) = 4×2 - 3×2 = 8 - 6 = 2

b)

$(A - 2I_{2}) \cdot (A - 4I_{2}) = \left(\begin{array}{ccc}4 - 2 \cdot 1&2 - 2 \cdot 0\\3 - 2 \cdot 0&2 - 2 \cdot 1\end{array}\right) \cdot \left(\begin{array}{ccc}4 - 4 \cdot 1&2 - 4 \cdot 0\\3 - 4 \cdot 0&2 - 4 \cdot 1\end{array}\right) =$

$= \left(\begin{array}{ccc}4 - 2&2 - 0\\3 - 0&2 - 2\end{array}\right) \cdot \left(\begin{array}{ccc}4 - 4&2 - 0\\3 - 0&2 - 4\end{array}\right)$

$= \left(\begin{array}{ccc}2&2\\3&0\end{array}\right) \cdot \left(\begin{array}{ccc}0&2\\3&-2\end{array}\right)$

$= \left(\begin{array}{ccc}2 \cdot 0 + 2\cdot 3&2 \cdot2 + 2\cdot ( - 2)\\3 \cdot0 + 0\cdot 3&3 \cdot 2+ 0 \cdot ( - 2)\end{array}\right)$

$= \left(\begin{array}{ccc}0 + 6&4 - 4\\0 + 0&6 + 0\end{array}\right) = \left(\begin{array}{ccc}6&0\\0&6\end{array}\right)$

$= 6 \cdot \left(\begin{array}{ccc}1&0\\0&1\end{array}\right) = 6 \cdot I_{2}$

q.e.d.