Question

eu am luat 1,2,3,4,5,6,7,8,9.Banuiesc ca exista o formula,nu stai sa faci asa.Totusi,dacă scriu asa oare se puncteaza la bac ? (supunctul c)​
#matrice 50puncte

Answer 1

c)  Membrul stâng al ecuației va fi o matrice de forma

$\it \begin{pmatrix} a_{11&a_{12}\\ \\ a_{21}&a_{22}}\end{pmatrix},\ \ \ unde:\\ \\ \\ a_{11}=2\cdot1+1+2\cdot2+1+2\cdot3+1+\ ...\ +2\cdot9+1=\\ \\ =3+5+7+\ ...\ +19=10^2-1=99\\ \\ \\ a_{12}=1+2+3+\ ...\ +9=45\\ \\ \\ a_{21}=\underbrace{\it1+1+1+\ ...\ +1}_{9\ termeni}=9\\ \\ \\ a_{22}=2+3+4+\ ...\ +10=55-1=54$

Ecuația  devine:

$\it \begin{pmatrix} \it99&\it45\\ \\ \it9&\it54\end{pmatrix}=9B(x) \Rightarrow 9\cdot\begin{pmatrix} \it11&\it5\\ \\ \it1&\it6\end{pmatrix}=9B(x)\bigg|_{:9} \Rightarrow \begin{pmatrix} \it11&\it5\\ \\ \it1&\it6\end{pmatrix}=\begin{pmatrix} \it2x+1&\it x\\ \\ \it1&\it x+1\end{pmatrix}\Rightarrow \\ \\ \\ \Rightarrow x=5$