MATRICES INVERSAS PROBLEMA 1 A=

A= -20+72+24-90-12+32 = 6 A11= (5 · -2)- (1 · 6) = -10-6 = 16 A12= - - [(4 · -2)- (3 · 6)] = 8 + 18 = 26 A13= (4 · 1)- (3 · 5)= 4 - 15 = -11 A21= - - [(4 · -2)- (1 · 6)] = 8 + 6 = 14 A22= (2 · -2)- (3 · 6) = -4 - 18 = -22 A23 = - - [(2 · 1)- (3 · 4)] = -2 + 12 = 10 A31= (4 · 6)- (5 · 6) = 24 - 30 = -6 A32 = - - [(2 · 6)- (4 · 6)] = -12 + 24 = 12

2 4 6 4 5 6 3 1 -2

2 4 6 2 4

4 5 6 4 5

3 1 -2 3 1

5 6

1 -2

4 6

3 -2

4 5

3 1

4 6

1 -2

2 6

3 -2

2 4

3 1

4 6

5 6

2 6

4 6

A-1 =

-16 (2) + 14 (4) -6 (3) = 6 -16 (4) + 14 (5) -6 (1) = 0 -16 (6) + 14 (6) -6 (-2)= 0

-11 (2) + 10 (4) -6 (3) = 0 -11 (4) + 10 (5) -6 (1) = 0 -11 (6) + 10 (6) -6 (-2)= 6

26 (2) -22 (4) +12 (3) = 0 26 (4) -22 (5) +12 (1) = 6 26 (6) -22 (6) +12 (-2)= 0

A-1 =

A-1 =

PROBLEMA 2

A =

A= -3 + 2 - 6 - 1 = -8 A11 = (-1 · 1)- (1 · 2) = -1-2 = -3 A12 = - - [(1 · 1)- (1 · 2)] = -1 + 2 = 1 A13 = (-1 · 1)- (1 · 2) = -1-2 = -3

2 4 6 4 5 6 3 1 -2

-16 14 -6 26 -22 12 -11 10 -6

6 0 0 0 6 0 0 0 6

1 0 0 0 1 0 0 0 1

3 1 0 1 -1 2 1 1 1

3 1 0 3 1

1 -1 2 1 -1

1 1 1 1 1

-1 2

1 1

1 2

1 1

1 2

1 1

A21= - - [(1 · 1)- (1 · 0)] = -1 + 0 = -1 A22= (3 · 1)- (1 · 0) = 3 - 0 = 3 A23= - - [(3 · 1)- (1 · 1)] = -3 + 1 = -2 A31= (1 · 2)- (-1 · 0) = 2 - 0 = 2 A32= - - [(3 · 2)- (1 · 0)] = -6 - 0 = -6 A33= (3 · -1)- (1 · 1) = -3 - 1 = -4

A-1 =

-3(3) -1 (1) + 2(1) = -8 -3(1) - 1(-1) + 2(1) = 0 -3(0) - 1(2) + 2(1)= 0

1(3) + 3(1) - 6(1) = 0 1(1) + 3(-1) - 6(1) = -8 1(0) + 3(2) - 6 (1)= 0

2(3) - 2(1) - 4(1) = 0 2(1) - 2(-1) - 4(1) = 0 2(0) - 2(2) - 4(1)= -8

A-1 =

A-1 =

1 0

1 1

3 0

1 1

3 1

1 1

1 0

-1 2

3 0

1 2

3 1

1 -1

-3 -1 2 1 3 -6 2 -2 -4

3 1 0 1 -1 2 1 1 1

-8 0 0 0 -8 0 0 0 -8

-1 0 0 0 -1 0 0 0 -1

PROBLEMA 3

A=

A= 2 + 3 - 2 - 4 = -1 A11= (1 · 2)- (1 · 2) = 2-2 = 0 A12 = - - [(1 · 2)- (0 · 2)] = -2 - 0 = -2 A13= (1 · 1)- (0 · 1) = 1- 0 = 1 A21= - - [(2 · 2)- (1 · 3)] = -4 + 3 = -1 A22= (1 · 2)- (0 · 3) = 2 - 0 = 2 A23= - - [(1 · 1)- (0 · 1)] = -1 - 0 = -1 A31= (2 · 2)- (1 · 3) = 4 - 3 = 1 A32= - - [(1 · 2)- (1 · 3)] = -2 +3 = 1 A33= (1 · 1)- (1 · 2) = 1 - 2 = -1

1 2 3 1 1 2 0 1 2

1 2 3 1 2

1 1 2 1 1

0 1 2 0 1

1 2

1 2

1 2

0 2

1 1

0 1

2 3

1 2

1 3

0 2

1 2

0 1

2 3

1 2

1 3

1 2

1 2

1 1

A-1 =

-1 (1) + 1(0) = -1 - 1(1) + 1(1) = 0 - 1(2) + 1(2)= 0

-2(1) + 2 (1) + 1(0) = 0 -2(2) + 2(1) + 1(1) = -1 -2(3) + 2(2) + 1(2)= 0

1(1) - 1 (1) - 1(0) = 0 1(2) - 1(1) - 1(1) = 0 1(3) - 1(2) - 1(2)= -1

A-1 = 1 A-1 =

0 -1 1 -2 2 1 1 -1 -1

1 2 3 1 1 2 0 1 2

-1 0 0 0 -1 0 0 0 -1

-1 0 0 0 -1 0 0 0 -1