m10 (2)

Rozdział 2

10. Rozwiązać równania macierzowe z niewiadomą macierząX:

1 0 -2

A =    12    3

a )AX-B= C

A-¹1    = C + 5

X= A~^X(C + B) Wyznaczmy macierz ,4^_1

10-2 10 12    3    1    2    ^;

-1 -1 -1 -1 -1 -2 + 2-4 + 3 = -1*0

2    3

= (-D

Au = (-D

^13 = (-1)

A21 = (-1)

^22 = (-1)

^23 = (-1)

Asi = (-D

As 2 = (-1)

-1 -1

1    3

-1 -1

1 2 -1 -1

0 -2 -1 -1

1 -2 -1 -1

1 0 -1 -1

0 -2

2 3

1 -2 1    3

1 0 1 2

= 1

= -2

= 1

= 2

= -3

= 1

= 4

= -5

B =

C =

-1 -	1 -	1
0 2	-2
5 1	0
0 -3	1
-12	0	6
7	-2	0
0	0	-1

^33 = (-1)

= 2

	1 -2 1	T	1 2 4
A^d =	2 -3 1	=	-2 -3 -5
	4-5 2		1 1 2

1    2    4

A'¹ = (-1)

-2 -3 -5 1 1 2

-1 -2 -4 2    3    5

-1 -1 -2

	-12	0	6
C + B =	7	-2	0	+
	0	0	-1

0 2-2 5    1    0

0 -3    1

-12 2    4

12 -1 0 0-3 0

	r i <N I T—H 1 1_		-12 2 4
X =	2 3 5	•	12 -1 0
	-1 -1 -2		0-3 0

-12    12    -4

12    -14    8

0    5-4

d) A-XC = BC -XC = 5C-.4 XC = -BC + A X= (~BC + A)C-¹ Wyznaczmy macierz C^_1

C =

-12	0	6	-12	0
7	-2	0	7	_2 = -24 * 0
0	0	-1	0	0

-2 0 0 -1

= 2

Cu = (-D

C12 = (-1)

Cl3 = (-1)

C21 = (-1)

C22 = (-1)

C23 = (-1)

C31 = (-1)

7 0 0 -1

7 -2 0 0

0 o

o -1

-12 6 0 -1

-12 0 0 0

0 6 -2 0

= 7

= 0

= 0

= 12

= 0

= 12