Question

ofer coroană
ex 1 tot​

Answer 1

Răspuns:

a)

$\det(A^t)\det A=\begin{vmatrix}1 & 1 & 0\\0 & 0 & 1\\0 & 1 & 0\end{vmatrix}=\begin{vmatrix}0 & 1\\1 & 0\end{vmatrix}=-1$

b)

$A^2=\begin{pmatrix}1 & 1 & 1\\0 & 1 & 0\\0 & 0 & 1\end{pmatrix}, \ A^3=A^2\cdot A=\begin{pmatrix}1 & 2 & 1\\0 & 0 & 1\\0 & 1 & 0\end{pmatrix}$

c)

$A^2+A=\begin{pmatrix}1 & 1 & 1\\0 & 1 & 0\\0 & 0 & 1\end{pmatrix}+\begin{pmatrix}1 & 1 & 0\\0 & 0 & 1\\0 & 1 & 0\end{pmatrix}=\begin{pmatrix}2 & 2 & 1\\0 & 1 & 1\\0 & 1 & 1\end{pmatrix}$

$A^3+I_3=\begin{pmatrix}2 & 2 & 1\\0 & 1 & 1\\0 & 1 & 1\end{pmatrix}+\begin{pmatrix}1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{pmatrix}=\begin{pmatrix}2 & 2 & 1\\0 & 1 & 1\\0 & 1 & 1\end{pmatrix}$

Se observă că rezultatele sunt egale.

P.S. Păstrează-ți coroana!

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