O matrice este simetrica daca este egala cu transpusa sa.(transpusa este cea in care liniile devin coloane)
[tex]A=\left[\begin{array}{ccc}4&3+a&b\\2a^2&1&-10\\2&c-2&2\end{array}\right]=\left[\begin{array}{ccc}4&2a^2&2\\3+a&1&c-2\\b&-10&2\end{array}\right] <=>4=4(A) ~\\2a^2=a+3=>2a^2-a-3=0 <=>2a^2+2a-3a-3=0<=>2a(a+1)-3(a+1)=0<=>(2a-3)(a+1)=0=>a_1=\frac{3}{2}~a_2=-1\\~\\b=2~\\c-2=-10 =>c=-8[/tex]
