Question

Determine a matriz inversa de:
|5 8|
|2 3| ????

Answer 1

{5a+8b = 1 ×(-2)
{2a+3b = 0 ×5

{-10a-16b = -2
{10a+15b = 0

-b = -2 ×(-1)
➩ b = 2

2a+3b = 0
2a+3×2 = 0
2a+6 = 0
2a = -6
a = -6⁄2
➩ a = -3

{5c+8d = 0 ×(-2)
{2c+3d = 1 ×5

{-10c-16d = 0
{10c+15d = 5

-d = 5 ×(-1)
➩ d = -5

2c+3d = 1
2c+3(-5) = 1
2c-15 = 1
2c = 1+15
2c = 16
c = 16⁄2
➩ c = 8


Resposta:

|-3 8|
|2 -5|