Question

Uma matriz qudrada A é chamada matriz antissimetrica se, ela for igual à aposta de sua transposta, isto é , A = -A^t. Para que seja antissimetrica a matriz: 


$\left[\begin{array}{ccc}a-b&a-3\\c+b&a-1\\\end{array}\right]$
A soma a+b+c deve ser igual a : R:3 .-. 

minha dúvida e como saber valor de A B C eu tento igualar mas nunca da certo =s obrigado!!!

Answer 1

$A=\left[\begin{array}{cc}a-b&a-3\\c+b&a-1\end{array}\right]\\\\\\A^{T}=\left[\begin{array}{cc}a-b&c+b\\a-3&a-1\end{array}\right]\\\\-A^{T}=-\left[\begin{array}{cc}a-b&c+b\\a-3&a-1\end{array}\right]\\\\-A^{T}=\left[\begin{array}{cc}b-a&-c-b\\3-a&1-a\end{array}\right]$
_____________________

$A=-A^{T}\\\\\left[\begin{array}{cc}a-b&a-3\\c+b&a-1\end{array}\right]=\left[\begin{array}{cc}b-a&-c-b\\3-a&1-a\end{array}\right]\\\\a-b=b-a\\a+a=b+b\\2a=2b\\a=b\\\\a-3=-c-b\\a+b=-c+3\\a+a=-c+3\\2a=-c+3\\2a+c=3\\c=3-2a$

$a-1=1-a\\a+a=1+1\\2a=2\\a=1$

Podemos achar os valores de b e c:

$b=a\\b=1\\\\c=3-2a\\c=3-2.1\\c=3-2\\c=1$

$a+b+c=1+1+1\\a+b+c=3$