Question

Dada a matriz n= $\left[\begin{array}{ccc}3&-1&2\\5&0&4\\7&-2&6\end{array}\right]$ , calcular os cofatores:

a)$n_{12}$

b)$n_{32}$

c)$n_{23}$

Answer 1

Olá

Para encontrar a matriz dos cofatores vc tem que eliminar a linha e a coluna da matriz... Por exemplo n12, vc tem q eliminar a 1 linha e a 2 coluna, irá restar um matriz 2x2, vc calcula o determinante e multiplica por (-1) elevado a i+j


a) 

$n12=(-1)^1^+^2\cdot \left[\begin{array}{ccc}5&4\\7&6\\\end{array}\right] ~=(-1)^3\cdot(30-28)~=~-1\cdot(2)~=~\boxed{\boxed{-2}}$


b)

$n32=(-1)^3^+^2\cdot \left[\begin{array}{ccc}3&2\\5&4\\\end{array}\right] ~=(-1)^5\cdot(12-10)~=~-1\cdot(2)~=~\boxed{\boxed{-2}}$


c)

$n23=(-1)^2^+^3\cdot \left[\begin{array}{ccc}3&-1\\7&2\\\end{array}\right] ~=(-1)^5\cdot(6-(-7))~= \\ \\ \\ ~~~~~~~ ~~~~~~ ~~~~~~ ~ ~~~~ ~~~~ ~~~~ ~~~~ ~~~~-1\cdot(13)~=~\boxed{\boxed{-13}}$