Question

PUNCTUL C VA ROGGG!!!!!​

Answer 1

Răspuns:

c). n = 3

Explicație pas cu pas:

Nu pot face paranteze rotunde la matrice, cand copieze rezolvarea le faci tu rotunde.

$A(n)*A(2-n) = 2*A(-6)$

deci:

$\left[\begin{array}{cc}n&3\\-3&n&\end{array}\right] *\left[\begin{array}{cc}2-n&3\\-3&2-n&\end{array}\right] =2*\left[\begin{array}{cc}-6&3\\-3&-6&\end{array}\right]$

$\left[\begin{array}{cc}n*(2-n)+3*(-3)&n*3 + 3*(2-n)\\-3*(2-n)+n*(-3)&-3*3+n*(2-n)&\end{array}\right] =\left[\begin{array}{cc}2*(-6)&2*3\\2*(-3)&2*(-6)&\end{array}\right]$

$\left[\begin{array}{cc}2*n-n^2 -9&3*n + 6- 3*n\\-6 + 3*n -3*n&-9+2*n - n^2)&\end{array}\right] =\left[\begin{array}{cc}-12&6\\-6&-12&\end{array}\right]$

$\left[\begin{array}{cc}-n^2 +2*n-9&6\\-6&- n^2+2*n-9 )&\end{array}\right] =\left[\begin{array}{cc}-12&6\\-6&-12&\end{array}\right]$  

⇔ -n² +2n - 9 = -12

-n² +2n - 9 + 12 = 0

-n² +2n + 3 = 0

n² -2n - 3 = 0

n² -3n + n - 3 = 0

n(n - 3) + n - 3 = 0

(n - 3)(n + 1) = 0 ⇔ n - 3 = 0 sau n + 1 = 0

n - 3 = 0 ⇒ n = 3

n + 1 = 0 ⇒ n = -1 ∉ N