Question

8. Uma matriz A é simétrica se, e somente se, A = A^t.
Determine "a" para que A = (1 a^2) (a 2 ) seja simétrica.​

Answer 1

$A=\left[\begin{array}{cc}1&a^{2}\\a&2\end{array}\right]$

$A^{t}=\left[\begin{array}{cc}1&a\\a^{2}&2\end{array}\right]$

$A=A^{t}\\\\\\\left[\begin{array}{cc}1&a^{2}\\a&2\end{array}\right]=\left[\begin{array}{cc}1&a\\a^{2}&2\end{array}\right]$

$a^{2} =a\\\\a^{2} -a=0\\\\a(a-1)=0$

$a=0\\\\ou\\\\a-1=0\\\\a=1$

Então, a matriz A será simétrica se a=0 ou a=1.