Задания - 2004 / Задания / Job-4

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич	1
Матричные операции.

Вычислите значение матричного выражения R. Сохраните промежуточные вычисления. Составите программу, для вычисления R, используя язык программирования VBA. Проведите расчет по программе и сравните результаты. Операция sled([матрица]) – сумма диагональных элементов матрицы.

Пример.

R =		=		=	→	= →
		A B c+				A d
=	2		1 1			=		1			2			2				3
													→			→
A =					;	B = 3					1 ;		c	=	;	d	=	1
	1		3 2					4			1			3				2
		= =			2	1 1				1		2		9		6
=
RM =		A B		= 1		3 2				3		1 = 18				7
										4		1
=		=		→		9 6			2			36
RV	= RM c				=						=
					18		7		3			57
		=			2	1 1					3		9
=			→
RV1 =		A d		= 1		3 2				1 =			10
										2
=			=		=		9			36			=	45
RV1 =		RV1+ RV =							+
						10				57				67
R =	∑2		rv1i		=	452	+672				=80.709
	i =1

Option Explicit

Option Base 1 Sub main()

Dim A!(2, 3), B!(3, 2), c!(2), D!(3), RM!(2, 2), RV!(2), RV1!(2) Dim i%, j%, l%, k!, s!, R!

'Ввод элементов матрицы A For i = 1 To 2

For j = 1 To 3

A(i, j) = Cells(i + 4, j) Next j

Next i

'Ввод элементов матрицы B For i = 1 To 3

For j = 1 To 2

B(i, j) = Cells(i + 4, j + 4) Next j

Next i

'Ввод элементов вектора C For i = 1 To 2

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич

2

C(i) = Cells(i + 4, 8)

Next i

'Ввод элементов вектора D For i = 1 To 3

D(i) = Cells(i + 4, 10) Next i

'Вычисление матрицы RM=A*B For i = 1 To 2

For j = 1 To 2 s = 0

For l = 1 To 3: s = s + A(i, l) B(l, j): Next l RM(i, j) = s

Next j Next i

'Вычисление вектора RV=RM*C For i = 1 To 2

s = 0

For l = 1 To 2: s = s + RM(i, l) * C(l): Next l RV(i) = s

Next i

'Вычисление вектора RV1=A*D

For i = 1 To 2 s = 0

For l = 1 To 3: s = s + A(i, l) * D(l): Next l RV1(i) = s

Next i

'Вычисление RV1=RV1+RV

For i = 1 To 2: RV1(i) = RV1(i) + RV(i): Next i 'Вычисление нормы вектора ||RV1||

s = 0: For i = 1 To 2: s = s + RV1(i) * RV1(i): Next i R = Sqr(s)

Cells(2, 5) = R End Sub

Задания.

1)

R =

=

=

→

−

→

A B c

d

3

=

1

2 8

=

7

1

→

5

→

A

=

;

B

= 4

4 ;

c

= ;

d

= 5

4

2 3

1

4

9

6

2) R =

=

T

=

=

= T

→

−

→

A

A− B B

d

c

=

1

8 5

=

5

4

7

7

→

→

A

=

;

B

= 4

3 ;

c

= ;

d

=

1

6

2 6

9

3

2

2

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич

3

3) R =

→T

=

= T

→T

=

c

A

A −d B

=

2 4

3

=

3

7

9

3

=

→

→

=

A

=

;

B

5

2 ;

c

= ;

d

5

8 3

9

8

3

3

7

4) R =

→T

=

= T

→T

= →

d

B B

+ c

A d

1

1

7

=

3 1

9

=

3

→

→

A

=

;

B

=

6

1 ;

c

= ;

d

=

9

1 3

3

7

2

5

4

→T

→

→T

= T

=

→

5) R = c c

−d

A A d

=

3 7

6

=

8

4

5

3

→

→

A

=

;

B

=

7

9 ;

c

= ;

d

=

4

3 3

6

6

2

6

9

6) R =

=

= →

→

+

→

A B c

d

c

8

=

4 3

3

=

7

7

7

→

→

A

=

;

B

=

8

8 ;

c

= ;

d

=

9

5 4

1

6

2

7

5

7) R =

=

= →

−

=

=

→

A B c

B A d

3

=

4 9

1

=

5

1

1

→

→

A

=

;

B

=

9

7 ;

c

= ;

d

=

4

7 4

4

5

1

9

1

8) R =

→T

=

=

→T

→T

→

d

B−

A d

− c c

=

5 6

7

=

3

3

3

8

→

→

A

=

;

B

=

1

6 ;

c

= ;

d

=

8

9 4

7

4

1

1

6

9)

= T

=

−

=

T =

R = sled A

A

B

B

=

6 3

4

=

1

6

5

3

→

→

A

=

;

B

=

2

5 ;

c

= ;

d

=

4

2 5

1

3

9

3

2

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич

4

10)

=

=

= =

=

T

=

R = sled A B

−sled B

A− A

A

=

6 8

1

=

8

9

7

8

→

→

A =

;

B

=

3

4 ;

c

= ;

d

=

8

4 5

4

3

9

4

7

11)

=

→

T

→

+

=

R = A d

c

B

=

7 5

8

=

6

3

1

3

→

→

A =

;

B

=

4

3 ;

c

= ;

d

=

3

6 6

7

2

8

6

3

12)

=

→ T

→

+

=

R = B c

d

A

=

8 2

5

=

4

6

3

8

→

→

A =

;

B

=

5

2 ;

c

= ;

d

=

7

9 6

2

1

8

7

9

13)

R =

→ →T

+

→ →T

c d

d

c

2

9

5

4

=

8 7

2

=

→

→

A =

;

B

=

5

1 ;

c

= ;

d

=

3

2 6

5

9

7

9

5

14)

R =

→ →T

T

→

+

=

=

c d

c

A B

=

9 4

8

=

9

3

8

8

→

→

A =

;

B =

6

9 ;

c

= ;

d

=

7

4 7

8

8

7

1

1

15)

R =

→ →T

T

→

+

=

=

d

c

d

A B

=

1 1

6

=

7

6

1

4

→

→

A =

;

B

=

7

8 ;

c

= ;

d

=

2

6 7

2

8

6

3

6

=

= T

→ T

→

=

16)

c+

A

R =

A+ B d

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич

5

=	1	6	3	=	6	8
A =		7	;	B =	8	7 ;
	8		5		7	6
			=	= T	→ T	→
17)			A−			c+
	R =			B d
=	2	3	9	=	4	2
A =		8	;	B =	9	6 ;
	1		8		6	5
			=	= T	→ T	→
18)			B+			d +
	R =			A c
=	2	9	6	=	2	5
A =		8	;	B =	1	5 ;
	3		3		5	5
			=	= T	→ T	→
19)			B−			d +
	R =			A c
=	3	5	4	=	9	8
A =		8	;	B =	2	3 ;
	5		6		5	4

=T → = = =

20)R = A c+ B A B

=	4	2			1			=			7	2
A =		9				;		B		=	3	2 ;
	7				9						4	4
21)	R =				=	→		=	T		= T	→
					A d		+ B				A	c
=	4	8			7			=			5	5
A =		9				;		B		=	4	1 ;
	9				3						3	3
22)	R =				=	T	→	+	=	=		→
					B	d			A B c
=	5	5			4			=			3	8
A =		9				;		B		=	5	9 ;
	2				6						2	3

c = 3 ;

8

d = 7

→

→

4

2

=

A

6 ;

4

→

=

→

= 2

c

d

6

7

=

B

8 ;

8

→

=

→

= 6

c

d

7

3

=

B

4

c = 1 ;

d = 1

→

→

9

9

c = 4 ;	9
	d = 6
→	→
1	5

c = 6 ;	4
	d = 1
→	→
3	1

c = 8 ;	9
	d = 5
→	→
4	6

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич

6

23)	R =		= →		= T		= T	→
			B c	+ A B				d
=	6	1	2		=		1	2			2
										→
A =		1	;		B	=	6	8 ;		c	= ;
	4		9				1	2			6

24)

→T

=

→T

= →

R = c

A+d

B c

=

6 7

8

=

8

5

4

→

A =

;

B

=

7

7 ;

c

= ;

6 1

4

1

2

7

25)

→

→T

=

=

+

=

R = sled

c d

+ A

B

B

=

7 4

5

=

6

7

6

→

A =

;

B

=

7

6 ;

c

= ;

8 1

7

9

1

9

26)

→

→T

=

=

+

=

R = sled

d

c

+ B

A

A

=

7 9

2

=

5

1

9

→

A =

;

B

=

8

5 ;

c

= ;

1 2

1

8

1

1

27)

R =

→

→T

= T

=

c d

+ A

+ B

4 d→ = 12

9 d→ = 57

4 d→ = 93

9 d→ = 48

=	8 6			9	=		3		4			2			5
											→		→
A =				; B		= 9			4 ;		c	= ;	d	=	9
	3 2			4			7		9			2			5
28)	R =			→	→T	=	T	+	=
			d c + B						A
=	1 8		2		=		2		9			1			8
											→		→
A =				; B		=	8		1 ;		c	= ;	d	=	3
	1 1		8				3		7			5			3
29)		→T			→ →T		=	T	→
	R = d			c d		+ A			c

(С) ИиКМ РХТУ январь 2004г. Калинкин Владимир Николаевич

7

=	1	1	9		=		1		6
A =		1		; B		=	9		9 ;
	2		9				7		3
30)		→T		→ →T		+	=		→
	R = c			c d			A	d
=	2	4	8		=		9		3
A =		2		; B		=	9		9 ;
	3		2				2		7
31)		→T	→ →T			+	= T		→
	R = c		d c				B		d
=	2	7	6		=		8		9
A =		2		; B		=	1		8 ;
	4		3				6		2
32)		→T			→ →T	+	=		→
	R = d			d c			B		c
=	2	1	5		=		7		6
A =		2		; B		=	1		8 ;
	5		5				1		7

	7			1
→		→	=
c	= ;	d		5
	2			5

c = 3 ;	3
	d = 7
→	→
7	8

c = 9 ;	6
	d = 9
→	→
3	2

c = 6 ;	8
	d = 2
→	→
8	4