Determine a matriz inversa da matriz M=(-1 2 -1 3)
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M =
|-1 2| |a c| |1 0|
|-1 3| × |b d| = |0 1|
{-a+2b = 1 ×(-1)
{-a+3b = 0
•b = -1
-a+2b = 1
-a+2(-1) = 1
-a-2 = 1
-a = 1+2
-a = 3 ×(-1)
•a = -3
{-c+2d = 0 ×(-1)
{-c+3d = 1
•d = 1
-c+2d = 0
-c+2 = 0
-c = -2 ×(-1)
•c = 2
Resposta:
|-3 2|
|-1 1|
|-1 2| |a c| |1 0|
|-1 3| × |b d| = |0 1|
{-a+2b = 1 ×(-1)
{-a+3b = 0
•b = -1
-a+2b = 1
-a+2(-1) = 1
-a-2 = 1
-a = 1+2
-a = 3 ×(-1)
•a = -3
{-c+2d = 0 ×(-1)
{-c+3d = 1
•d = 1
-c+2d = 0
-c+2 = 0
-c = -2 ×(-1)
•c = 2
Resposta:
|-3 2|
|-1 1|
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