m9 (2)

Rozdział 2

Macierz odwrotna macierzy A: (dla det^4 * 0)

A-¹ = -±--A^D

det A

9. Wyznaczyć macierz odwrotną do:

-i T i-

A^d =

A-¹

C) ą =

-3

6

2    3

3    5

2    3

3    5

2    3

3    5

2    3

3    5

-3

6

-2

4

-2

4

= 0 =>Macierz odwrotna nie istnieje

a)
A =	5 -3	-3 2
5	-3	= 10-

-3 2

= (-i)¹⁺¹ -|2| = 2 Au = (-l)¹⁺²-|-3| = 3 A-21 = (-1)²⁺¹ -|—31 = 3 A 22 = (-l)²⁺²-|5| = 5

e)

A =

-1 1

4

-12 0 1    2    4

4-3 0

2 0 2 4 -3 0

-1 2

1    2    = 32- 12 = 20 *0

4 -3

A u = (-1)²'

2 4 -3 0

= 12

A12 = (-1)³'

1 4

4 0 = 16

= -11

A 21 = (-1)³'

^22 = (-1)⁴'

A 23 = (-1)⁵'

A 31 = (-I)⁴'

A 32 = (-1)⁵'

2 0 -3 0

-1 0 4    0

-1 2 4 -3

2 0 2 4

-1 0 1    4

= 0

= 0

= 5

= 8

= 4

= -4

-i T

-1    2

1    2

12 16 -11

A^d =

0    0    5

8    4-4

12 0 8 16    0 4

-11 5-4

A-¹ = —■

^A 20

12 0 8 16 0 4 -11 5-4

n

0

20

0

1

2

2

4 -3