Добавил:

ivanov666 Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Башкирский Государственный Аграрный Университет

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

Аналитическая геометрия и линейная алгебра. Учебное пособие

.pdf

Скачиваний:

Добавлен:

12.08.2026

Размер:

963 Кб

Скачать

☆

<<< < Предыдущая 1 2 3 4 5 6 7 89 / 129 10 11 12 > Следующая >>>

§8 7 7·

§3 9 9·

§2·

0¸

7¸

0¸

D 7 3 4

3 8

8¹

9¹

7¹

§8 9 1·

§0 6 3·

§5·

4¸

7¸

5¸

D 6 6 3

7 1

2¹

8¹

9¹

§9 2 0·

§1 5 2·

§2·

9¸

2¸

3¸

D 6 0 3

5¹

1¹

§7 9 9·

§1 4 2·

§9·

0¸

3¸

6¸

D 5 6 7

7¹

1¹

§1 5 9·

§1 4 5·

§6·

9 5¸

8 6 1¸

9¸

D 2 3 9

6¹

7 2¹

1¹

§4 0 3·

§5 3 8·

§2·

7¸

1¸

D 8 3 9

2 1

4¹

9¹

7¹

§7 3 0·

§4 1 3·

§6·

3¸

5¸

4¸

D 0 2 1

7¹

0¹

3¹

§2 4 1·

§1 1 7·

§4·

8¸

5¸

0¸

D 9 0 2

7¹

6¹

3¹

§1 1 9·

§5 9 6·

§1·

0 3 6¸

2¸

4¸

D 2 9 5

2 5

9¹

3¹

4¹

§1 3 7·

§7 5 1·

§4·

3¸

3 2

1¸

2¸

D 1 6 6

5¹

3 3¹

7¹

§4 2 8·

§7 2 8·

§8·

4¸

6¸

2¸

D 0 5 1

4¹

7¹

1¹

§3 6 4·

§5 7

2·

§6·

5¸

2 4

3¸

2¸

D 4 3 6

1¹

6 4¹

3¹

§4 7 7·

§7 1 3·

§6·

4¸

5 5 2¸

9¸

D 1 4 5

0¹

5 5 3¹

7¹

§2 4 7·

§6

7·

§4·

2¸

0 5¸

6¸

D 0 1 4

2¹

8¹

5¹

ǵȖȗȌȋȌȒȏșȌȒȏ

ɉɨɧɹɬɢɟ ɨɩɪɟɞɟɥɢɬɟɥɹ ɞɥɹ ɦɚɬɪɢɰ ɪɚɡɦɟɪɧɨɫɬɢ 2q2 ɢ 3q3 ɭɠɟ ɜɫɬɪɟɱɚ ɥɨɫɶɧɚɦɜɪɚɡɞɟɥɟ Ɍɟɩɟɪɶɦɵ ɨɩɪɟɞɟɥɢɦ ɟɝɨɞɥɹɩɪɨɢɡɜɨɥɶɧɨɣ ɤɜɚɞɪɚɬɧɨɣ ɦɚɬɪɢɰɵ

Ɉɩɪɟɞɟɥɟɧɢɟ ɉɭɫɬɶ A – ɤɜɚɞɪɚɬɧɚɹ nqn ɦɚɬɪɢɰɚ

a		a	.......	a	¬
	11	12		1n

		a	.......	a
a		a	.......	a
	21	22		2n
A					.
			.......
.... .....			.......	.....



		an2	.......
an1		an2	.......	ann ®

Ɉɩɪɟɞɟɥɢɬɟɥɟɦ ɧɚɡɵɜɚɟɬɫɹ ɮɭɧɤɰɢɹ ɨɬ ɷɥɟɦɟɧɬɨɜ ɷɬɨɣ ɦɚɬɪɢɰɵ ɨɛɨɡɧɚ ɱɚɟɦɚɹ det A ɢɥɢ A ɢ ɡɚɞɚɜɚɟɦɚɹ ɪɟɤɭɪɪɟɧɬɧɵɦ ɩɪɚɜɢɥɨɦ

1.ɟɫɥɢ n 1 ɬɨ det A a11;

2.ɩɪɢ n p2

	n
	det A a1 j ( 1) j 1 A1j ,	(3.4.1)

j 1

ɝɞɟ A1j – ɨɩɪɟɞɟɥɢɬɟɥɶɦɚɬɪɢɰɵ ɤɨɬɨɪɚɹɩɨɥɭɱɢɬɫɹ ɟɫɥɢɜɦɚɬɪɢɰɟ A ɜɵɱɟɪɤ ɧɭɬɶ ɫɬɪɨɤɭ ɫ ɧɨɦɟɪɨɦ 1 ɢ ɫɬɨɥɛɟɰ ɫ ɧɨɦɟɪɨɦ j .

Ɏɨɪɦɭɥɚ 4. ɧɚɡɵɜɚɟɬɫɹ ɮɨɪɦɭɥɨɣ ɜɵɱɢɫɥɟɧɢɹ ɨɩɪɟɞɟɥɢɬɟɥɹ ɪɚɡɥɨ ɠɟɧɢɟɦ ɩɨ ɩɟɪɜɨɣ ɫɬɪɨɤɟ

ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ 4.1), ɜɵɱɢɫɥɢɦ ɨɩɪɟɞɟɥɢɬɟɥɶ ɦɚɬɪɢɰɵ ɪɚɡɦɟɪɧɨ ɫɬɢ 2q2 :

	a11	a12	a a	22	a a	.	(3.4.2)
	a21	a22	11	22	12	21

ɉɪɢɦɟɪ1

1	2	1¸4 2¸3 2.
3	4

ɉɭɫɬɶ ɡɚɞɚɧɚ ɤɜɚɞɪɚɬɧɚɹ ɦɚɬɪɢɰɚ 3q3:

a		a	a	¬
	11	12	13

		a	a
A a		a	a	.
	21	22	23


		a32	a33
a31		a32	a33	®

ɑɬɨɛɵ ɜɵɱɢɫɥɢɬɶ ɨɩɪɟɞɟɥɢɬɟɥɶ ɷɬɨɣ ɦɚɬɪɢɰɵ, ɩɪɟɞɫɬɚɜɥɹɟɦ ɟɟɜ ɜɢɞɟɥɢ ɧɟɣɧɨɣ ɤɨɦɛɢɧɚɰɢɢ ɨɩɪɟɞɟɥɢɬɟɥɟɣ ɜɬɨɪɨɝɨ ɩɨɪɹɞɤɚ ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɜɵɱɢɫ ɥɢɬɶ ɩɨ ɮɨɪɦɭɥɟ 4.2):

det A a

a22

a23

a21

a23

a21

a22

a11 ¸a22 ¸a33 a11 ¸a23 ¸a32 a12 ¸a21 ¸a33

a12 ¸a23 ¸a31 a13 ¸a21 ¸a32 a13 ¸a22 ¸a31.

ɉɪɢɦɟɪ

1.	1	3	5		1 0		2	0		2	1
	1	3	5
	2	1	0	1¸		3¸			5¸
	1	3	2		3 2		1	2		1	3
	1	3	2

¸ ¸ ¸ .

2.	2	1	0		1	8		4	8		4	1
	2	1	0
	4	1	8	2¸			1¸			0¸
	3	1	1		1	1		3	1		3	1
	3	1	1

¸ ¸ .

Ⱥɧɚɥɨɝɢɱɧɨ ɩɪɢɜɵɱɢɫɥɟɧɢɢ ɨɩɪɟɞɟɥɢɬɟɥɟɣɛɨɥɶɲɟɝɨɪɚɡɦɟɪɚɦɵ ɩɨɫɥɟ ɞɨɜɚɬɟɥɶɧɨ ɩɨɧɢɠɚɟɦ ɪɚɡɦɟɪɧɨɫɬɶ ɩɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ

ɂɧɨɝɞɚ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɨɩɪɟɞɟɥɢɬɟɥɹ ɭɞɨɛɧɨ ɩɪɢɦɟɧɹɬɶ ɮɨɪɦɭɥɵ ɤɨɬɨ ɪɵɟ ɦɵ ɫɮɨɪɦɭɥɢɪɭɟɦ ɧɢɠɟ ɜ ɜɢɞɟ ɬɟɨɪɟɦ.

Ɍɟɨɪɟɦɚ Ɉɩɪɟɞɟɥɢɬɟɥɶ ɦɨɠɧɨ ɜɵɱɢɫɥɹɬɶ ɪɚɡɥɨɠɟɧɢɟɦ ɩɨ ɥɸɛɨɣ ɫɬɪɨɤɟ [1, 5]:

n
GHW A aij j i Aij	4.4)
j 1

ɝɞɟ Aij – ɨɩɪɟɞɟɥɢɬɟɥɶ ɦɚɬɪɢɰɵ ɤɨɬɨɪɚɹɩɨɥɭɱɢɬɫɹ ɟɫɥɢɜɦɚɬɪɢɰɟ A ɜɵɱɟɪɤ ɧɭɬɶ ɫɬɪɨɤɭ ɫ ɧɨɦɟɪɨɦ i ɢ ɫɬɨɥɛɟɰ ɫ ɧɨɦɟɪɨɦ j.

ɉɪɢɦɟɪɉɭɫɬɶ

							1			2		3¬


										0		0
							A 2			0		0	.


										5		1
							4			5		1	®
Ɍ ɤ ɜɬɨɪɚɹ ɫɬɪɨɤɚ ɦɚɬɪɢɰɵ ɫɨɞɟɪɠɢɬ ɬɨɥɶɤɨ ɨɞɢɧ ɧɟɧɭɥɟɜɨɣ ɷɥɟɦɟɧɬ
ɬɨ ɩɪɢɦɟɧɢɦ ɮɨɪɦɭɥɭ i 2.
	1	2	3			2	3					1	3			1	2


	2	0	0	2¸					0¸					0¸				34.
	4	5	1			5	1					4	1			4	5
	4	5	1
ɌɟɨɪɟɦɚɈɩɪɟɞɟɥɢɬɟɥɶ ɦɨɠɧɨ ɜɵɱɢɫɥɹɬɶ ɪɚɡɥɨɠɟɧɢɟɦ ɩɨ ɥɸɛɨɦɭ
ɫɬɨɥɛɰɭ [1, 5]:
								n
					GHW A aij j i Aij												.4.5)
								i 1
ɉɪɢɦɟɪɉɭɫɬɶ
							4			2		3¬


										5
							A 2			5		0.


										1
							3			1		0®
Ɍ ɤ ɬɪɟɬɢɣ ɫɬɨɥɛɟɰ ɦɚɬɪɢɰɵ ɫɨɞɟɪɠɢɬ ɬɨɥɶɤɨ ɨɞɢɧ ɧɟɧɭɥɟɜɨɣ ɷɥɟɦɟɧɬ
ɬɨ ɩɪɢɦɟɧɢɦ ɮɨɪɦɭɥɭ 4.5),						j 3.
		4	2	3	¸	2	5	¸			4	2	¸		4	2



						3	1				3	1			2	5
		3	1	0
		3	1	0

ǸȉȕȐȘșȉȇ ȕȖȗȌȋȌȒȏșȌȒȌȐ [1, 5]

1.ȿɫɥɢ ɨɩɪɟɞɟɥɢɬɟɥɶ ɫɨɞɟɪɠɢɬ ɧɭɥɟɜɭɸ ɫɬɪɨɤɭ ɫɬɨɥɛɟɰ ɬɨ ɨɧ ɪɚɜɟɧ ɧɭɥɸ

2.ȿɫɥɢ ɞɜɟ ɫɬɪɨɤɢ ɫɬɨɥɛɰɚ ɨɩɪɟɞɟɥɢɬɟɥɹ ɫɨɜɩɚɞɚɸɬ ɬɨ ɨɩɪɟɞɟɥɢɬɟɥɶ ɪɚɜɟɧ ɧɭɥɸ

3.ȿɫɥɢ ɜɫɟ ɷɥɟɦɟɧɬɵ ɫɬɪɨɤɢ ɫɬɨɥɛɰɚ ɨɩɪɟɞɟɥɢɬɟɥɹ ɭɦɧɨɠɢɬɶ ɧɚ ɱɢɫɥɨ ɬɨ ɨɩɪɟɞɟɥɢɬɟɥɶ ɭɦɧɨɠɢɬɫɹ ɧɚ ɷɬɨ ɱɢɫɥɨ

4.ȿɫɥɢ ɩɨɦɟɧɹɬɶ ɦɟɫɬɚɦɢ ɞɜɟ ɫɬɪɨɤɢ ɫɬɨɥɛɰɚ ɨɩɪɟɞɟɥɢɬɟɥɹ ɬɨ ɨɩɪɟ ɞɟɥɢɬɟɥɶ ɫɨɯɪɚɧɢɬ ɚɛɫɨɥɸɬɧɭɸ ɜɟɥɢɱɢɧɭ ɚ ɡɧɚɤ ɩɨɦɟɧɹɟɬ ɧɚ ɩɪɨɬɢ ɜɨɩɨɥɨɠɧɵɣ

5.Ɉɩɪɟɞɟɥɢɬɟɥɶɬɪɚɧɫɩɨɧɢɪɨɜɚɧɧɨɣɦɚɬɪɢɰɵɪɚɜɟɧɨɩɪɟɞɟɥɢɬɟɥɸɦɚɬ ɪɢɰɵ det AT det A .

6.Ɉɩɪɟɞɟɥɢɬɟɥɶ ɩɪɨɢɡɜɟɞɟɧɢɹ ɤɜɚɞɪɚɬɧɵɯ ɦɚɬɪɢɰ ɪɚɜɟɧ ɩɪɨɢɡɜɟɞɟɧɢɸ ɨɩɪɟɞɟɥɢɬɟɥɟɣ GHW AB GHW AGHWB [1].

7.ȿɫɥɢ ɤ ɨɞɧɨɣ ɫɬɪɨɤɟ ɫɬɨɥɛɰɭ ɦɚɬɪɢɰɵ ɩɪɢɛɚɜɢɬɶ ɞɪɭɝɭɸ ɫɬɪɨɤɭ

ɫɬɨɥɛɟɰ ɭɦɧɨɠɟɧɧɭɸ ɧɚ ɱɢɫɥɨ ɬɨ ɜɟɥɢɱɢɧɚ ɨɩɪɟɞɟɥɢɬɟɥɹ ɧɟ ɢɡɦɟ ɧɢɬɫɹ

ɍɤɚɡɚɧɧɵɟ ɜɵɲɟ ɫɜɨɣɫɬɜɚ ɩɨɡɜɨɥɹɸɬ ɭɩɪɨɳɚɬɶ ɜɢɞ ɨɩɪɟɞɟɥɢɬɟɥɹ ɩɟɪɟɞ ɟɝɨ ɜɵɱɢɫɥɟɧɢɟɦ

ɉɪɢɦɟɪ ȼɵɱɢɫɥɢɦ ɨɩɪɟɞɟɥɢɬɟɥɶ ɦɚɬɪɢɰɵ

3		2	5	¬


	4	1	2
A	4	1	2	.


	3	1
	3	1	4®

Ȼɭɞɟɦ ɭɩɪɨɳɚɬɶ ɜɬɨɪɭɸ ɫɬɪɨɤɭ ɨɩɪɟɞɟɥɢɬɟɥɹ Ⱦɥɹ ɷɬɨɝɨ ɩɪɢɛɚɜɢɦ ɤ ɩɟɪ ɜɨɦɭ ɫɬɨɥɛɰɭ ɜɬɨɪɨɣ ɫɬɨɥɛɟɰ ɭɦɧɨɠɟɧɧɵɣ ɧɚ 4 ɤ ɬɪɟɬɶɟɦɭ ɫɬɨɥɛɰɭ ɩɪɢɛɚ ɜɢɦ ɜɬɨɪɨɣ ɫɬɨɥɛɟɰ ɭɦɧɨɠɟɧɧɵɣ ɧɚ 2 :

3 2 5 11 2 1 det A 4 1 2 0 1 0 .

3 1 4 1 1 6

Ɍɟɩɟɪɶ ɜɬɨɪɚɹ ɫɬɪɨɤɚ ɦɚɬɪɢɰɵ ɫɨɞɟɪɠɢɬ ɬɨɥɶɤɨ ɨɞɢɧ ɧɟɧɭɥɟɜɨɣ ɷɥɟɦɟɧɬ. ɉɪɢɦɟɧɢɦ ɮɨɪɦɭɥɭ i 2.

	11	2	1		2	1			11	1		11	2
	11	2	1
det A	0	1	0	0¸			1¸				0¸			67.
	1	1	6		1	6			1	6		1	1
	1	1	6
ȼɵɱɢɫɥɢɦ ɨɩɪɟɞɟɥɢɬɟɥɶ ɦɚɬɪɢɰɵ								1
					3	2	7	1
								¬

						4	1
					2	4	1	3
				A				.
						2	1
					3	2	1	1


						1	4
					2	1	4	2 ®

Ȼɭɞɟɦ ɭɩɪɨɳɚɬɶ ɱɟɬɜɟɪɬɵɣ ɫɬɨɥɛɟɰ ɨɩɪɟɞɟɥɢɬɟɥɹ Ⱦɥɹ ɷɬɨɝɨɩɪɢɛɚɜɢɦ ɤɨ ɜɬɨɪɨɣ ɫɬɪɨɤɟ ɨɩɪɟɞɟɥɢɬɟɥɹ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨɠɟɧɧɭɸ ɧɚ ɤ ɬɪɟɬɶɟɣ

ɫɬɪɨɤɟ ɩɪɢɛɚɜɢɦ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɤ ɱɟɬɜɟɪɬɨɣ ɫɬɪɨɤɟ ɩɪɢɛɚɜɢɦ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨɠɟɧɧɭɸ ɧɚ í2:

	3	2	7	1	3	2	7	1
det A	2	4	1	3	11	10	22	0	.
	3	2	1	1	6	4	8	0
	2	1	4	2	4 3 10			0

Ɍɟɩɟɪɶ ɱɟɬɜɟɪɬɵɣ ɫɬɨɥɛɟɰ ɦɚɬɪɢɰɵ ɫɨɞɟɪɠɢɬ ɬɨɥɶɤɨ ɨɞɢɧ ɧɟɧɭɥɟɜɨɣ ɷɥɟ ɦɟɧɬ. ɉɪɢɦɟɧɢɦ ɮɨɪɦɭɥɭ j 4 .

11 10 22 det A 6 4 8 ,

4 3 10

ɩɪɢɦɟɧɹɹ ɫɜɨɣɫɬɜɨ ɩɨɥɭɱɚɟɦ

11 10 22 det A 2 3 2 4 .

4 3 10

ɉɪɢɛɚɜɢɦ ɤ ɩɟɪɜɨɦɭ ɫɬɨɥɛɰɭ ɨɩɪɟɞɟɥɢɬɟɥɹ ɜɬɨɪɨɣ ɫɬɨɥɛɟɰ ɭɦɧɨɠɟɧɧɵɣ ɧɚ í ɤ ɬɪɟɬɶɟɦɭ ɫɬɨɥɛɰɭ – ɜɬɨɪɨɣ ɫɬɨɥɛɟɰ ɭɦɧɨɠɟɧɧɵɣ ɧɚ í2:

	1	10	2		0	8	2		8	2

det A 2	1	2	0	2	1	2	0	2			60.
	1	3	4		0	1	4		1	4

Ɍɟɤɫɬ ɡɚɞɚɧɢɹ ʋ ȼɵɱɢɫɥɢɬɶ ɨɩɪɟɞɟɥɢɬɟɥɶ ɦɚɬɪɢɰɵ A.

ȼɚɪɢɚɧɬɵ ɡɚɞɚɧɢɹ ʋ

§1 2 3·

§ 1 4 4·

§ 1 2 5 ·

2 3 5

2 3 7

2 3 1¸

3 5 1

§ 1 3

2 ·

§ 1 2 1·

§ 3 2 1·

2 2

2 3 4

2 3 3

3 5 3

§ 1 5

3 ·

§ 3 8 2 ·

§ 1 2 7·

2 3

1 3 1

2 3 3

3 5 6

....... a2n

....... a1n

§1 2 3·

§2 2 1 ·

§ 1 2 1·

4 2 4

1 3 0

5 3 1

8 5

3 7 3

§ 3 2 2·

§ 1 2 3 ·

4 1

2 3 7

1 3 3¸

1¸

3 5 8

§ 5 2 1·

§ 7 2

4 ·

§ 1 4 2 ·

1 1 2

3 1

2 3 5

3 5 3

3 5 6

12¹

§ 1 2 5·

§ 3 2 1 ·

§ 1 2 1·

2 4 5

2 5

1¸

4 1 1¸

3 5 2

3 5 3

§ ·

§ 2 1 4 ·

§ 1 2 4 ·

1 3 3

2 5 7¸

3 5 12

3 5 10

§ 1 2 2·

§ 2 2 7 ·

§ 1 2 3·

1 3

3 4 2

10 5 2¸

1¸

3 5 6

3 5 3

§ 1 2 5·

§ 3 2 1 ·

§ 1 2 2·

2 5 2

1 2 3

2 4 3¸

3 5 3

3 5

3 5 6

3.5. ǷȇȔȊ ȓȇșȗȏȝȢ

Ɋɚɫɫɦɨɬɪɢɦ ɦɚɬɪɢɰɭ A ɩɪɨɢɡɜɨɥɶɧɨɣ ɪɚɡɦɟɪɧɨɫɬɢ

a11

Aa21

....

am1

a12 a22

.....

am2

....... ..... ¬.

....... amn®

Ɉɩɪɟɞɟɥɟɧɢɟ 5 Ɋɚɧɝɨɦ ɦɚɬɪɢɰɵ ɨɛɨɡɧɚɱɚɟɦ rangA ɧɚɡɵɜɚɟɬɫɹ ɪɚɡ ɦɟɪɧɨɫɬɶ ɦɚɤɫɢɦɚɥɶɧɨɝɨɧɟɧɭɥɟɜɨɝɨɨɩɪɟɞɟɥɢɬɟɥɹ ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɧɚ ɫɬɪɨɤɚɯ ɢ ɫɬɨɥɛɰɚɯ ɞɚɧɧɨɣ ɦɚɬɪɢɰɵ ɇɟɧɭɥɟɜɨɣ ɨɩɪɟɞɟɥɢɬɟɥɶ ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɟɬ ɪɚɧɝ ɧɚɡɵɜɚɟɬɫɹ ɛɚɡɢɫɧɵɦ ɦɢɧɨɪɨɦ ɞɚɧɧɨɣ ɦɚɬɪɢɰɵ

ɉɪɢɦɟɪ5 Ɋɚɫɫɦɨɬɪɢɦ ɦɚɬɪɢɰɭ

0			3	0¬

		A		.

0 0 0®
		Ɉɱɟɜɢɞɧɨ ɱɬɨ rangA 1 ɛɚɡɢɫɧɵɣ ɦɢɧɨɪ ɫɨɫɬɨɢɬ ɢɡ ɨɞɧɨɝɨ ɷɥɟɦɟɧɬɚ
	3	3.
	3	3.
		Ɋɚɫɫɦɨɬɪɢɦ ɦɚɬɪɢɰɭ
2			0	0¬

		A		.
			0
0			0	4®

rangA 2 ɛɚɡɢɫɧɵɣ ɦɢɧɨɪ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɧɚ ɩɟɪɟɫɟɱɟɧɢɢ ɩɟɪɜɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɫɬɨɥɛɰɨɜ ɢ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɫɬɪɨɤɢ ɞɚɧɧɨɣ ɦɚɬɪɢɰɵ

02 04 8.

Ɉɩɪɟɞɟɥɟɧɢɟ 5 ɋɬɪɨɤɢ ɢ ɫɬɨɥɛɰɵ ɧɚ ɩɟɪɟɫɟɱɟɧɢɢ ɤɨɬɨɪɵɯ ɫɬɪɨɢɬɫɹ ɛɚɡɢɫɧɵɣ ɦɢɧɨɪ ɧɚɡɵɜɚɸɬɫɹ ɛɚɡɢɫɧɵɦɢ ɫɬɪɨɤɚɦɢ ɢ ɫɬɨɥɛɰɚɦɢ

Ɍɟɨɪɟɦɚ Ȼɚɡɢɫɧɵɟ ɫɬɪɨɤɢ ɫɬɨɥɛɰɵ ɥɢɧɟɣɧɨ ɧɟɡɚɜɢɫɢɦɵ Ʌɸɛɚɹ ɫɬɪɨɤɚ ɫɬɨɥɛɟɰ ɦɚɬɪɢɰɵ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧɚ ɜ ɜɢɞɟ ɥɢɧɟɣɧɨɣ ɤɨɦɛɢɧɚɰɢɢ ɛɚɡɢɫɧɵɯ ɫɬɪɨɤ ɫɬɨɥɛɰɨɜ [1, 5, 10].

ɗɥɟɦɟɧɬɚɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɦɚɬɪɢɰɵ

1.ɉɟɪɟɫɬɚɧɨɜɤɚ ɫɬɪɨɤ ɫɬɨɥɛɰɨɜ ɦɚɬɪɢɰɵ

2.ɍɦɧɨɠɟɧɢɟ ɫɬɪɨɤɢ ɫɬɨɥɛɰɚ ɧɚ ɱɢɫɥɨ ɨɬɥɢɱɧɨɟ ɨɬ ɧɭɥɹ

3.Ⱦɨɛɚɜɥɟɧɢɟ ɤ ɨɞɧɨɣ ɫɬɪɨɤɟ ɫɬɨɥɛɰɭ ɞɪɭɝɨɣ ɫɬɪɨɤɢ ɫɬɨɥɛɰɚ ɭɦɧɨ

ɠɟɧɧɨɣ ɧɚ ɱɢɫɥɨ Ɍɟɨɪɟɦɚ ɗɥɟɦɟɧɬɚɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɧɟ ɢɡɦɟɧɹɸɬ ɪɚɧɝ ɦɚɬɪɢɰɵ

[1, 10].

ɋɬɭɩɟɧɱɚɬɵɦ ɜɢɞɨɦ ɦɚɬɪɢɰɵ ɧɚɡɵɜɚɟɬɫɹ ɜɢɞ

a110

...

a12	...	a1k	...	a1l
0	...	a2k	...	a2l
0	...	0	...	a3l
0	...	0	...	0

...	...	...	...	...
...	...	...	...	...
0	...	0	...	0

... a1n

... a2n

... a3n

... a4n

... arn

... ...

... 0

¬.

Ɋɚɧɝ ɦɚɬɪɢɰɵ ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɝɞɚ ɦɚɬɪɢɰɚ ɢɦɟɟɬ ɫɬɭɩɟɧɱɚɬɵɣ ɜɢɞ Ɋɚɫɫɦɨɬɪɢɦ ɧɚɩɪɢɦɟɪ ɦɚɬɪɢɰɭ ɜɢɞɚ

a		a	a
	11	12	13
	0	a	a
	0	a	a
		22	23
A
	0	0	0
	0	0	0


	0	0	0
	0	0	0

Ɉɩɪɟɞɟɥɢɬɟɥɶ

a14 ¬

a24, ɝɞɟ a11a22a34 v0 .

a34

0 ®

a11 a12 a14

0 a22 a24 v0,

0 0 a34

ɚ ɨɩɪɟɞɟɥɢɬɟɥɶ ɜɫɟɣ ɦɚɬɪɢɰɵ det A 0 ɬ ɤ ɫɨɞɟɪɠɢɬ ɧɭɥɟɜɭɸ ɫɬɪɨɤɭ ɋɥɟ ɞɨɜɚɬɟɥɶɧɨ rangA 3.

ɉɪɟɨɛɪɚɡɨɜɚɧɢɹ – ɩɨɡɜɨɥɹɸɬ ɩɪɢɜɟɫɬɢ ɦɚɬɪɢɰɭ ɤ ɫɬɭɩɟɧɱɚɬɨɦɭ ɜɢɞɭ ɉɪɢɦɟɪ1. Ɋɚɫɫɦɨɬɪɢɦ ɦɚɬɪɢɰɭ

	1	2	3	4¬


		3	5
A 2		3	5	1.



	3	1	2
	3	1	2	3®

ɉɪɢɜɨɞɢɦ ɦɚɬɪɢɰɭ ɤ ɫɬɭɩɟɧɱɚɬɨɦɭ ɜɢɞɭ Ⱦɥɹ ɷɬɨɝɨ ɩɪɢɛɚɜɢɦ ɤɨ ɜɬɨɪɨɣ ɫɬɪɨɤɟ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨɠɟɧɧɭɸ ɧɚ ɤ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ ɩɪɢɛɚɜɢɦ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨɠɟɧɧɭɸ ɧɚ í3:

1	2	3 4¬		1 2	3	4	¬









			®				®

ɉɪɢɛɚɜɢɦ ɤ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ ɜɬɨɪɭɸ ɫɬɪɨɤɭ

1 2	3	4	¬	1 2 3 4¬







			®		®

Ȼɚɡɢɫɧɵɣ ɦɢɧɨɪ

10 72 7 v0.

Ʌɸɛɨɣ ɨɩɪɟɞɟɥɢɬɟɥɶ ɪɚɡɦɟɪɧɨɫɬɢ ɬɪɢ ɤɨɬɨɪɵɣ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɧɚ ɞɚɧ ɧɨɣ ɦɚɬɪɢɰɟ ɫɨɞɟɪɠɢɬ ɧɭɥɟɜɭɸ ɫɬɪɨɤɭ ɢ ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɪɚɜɟɧ ɧɭɥɸ ɉɨɥɭ ɱɚɟɦ rangA 2.

2. Ɋɚɫɫɦɨɬɪɢɦ ɦɚɬɪɢɰɭ

2	3	1	5¬


	3	1
4	3	1	2
A			.
	1	3
2	1	3	0


	7	3
8	7	3	7®

ɉɪɢɜɨɞɢɦ ɦɚɬɪɢɰɭ ɤ ɫɬɭɩɟɧɱɚɬɨɦɭ ɜɢɞɭ ɉɪɢɛɚɜɢɦ ɤɨ ɜɬɨɪɨɣ ɫɬɪɨɤɟ ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨɠɟɧɧɭɸ ɧɚ í ɤ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ – ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨ ɠɟɧɧɭɸ ɧɚ í ɤ ɱɟɬɜɟɪɬɨɣ ɫɬɪɨɤɟ – ɩɟɪɜɭɸ ɫɬɪɨɤɭ ɭɦɧɨɠɟɧɧɭɸ ɧɚ í4:

2 3	1 5¬		2 3 1 5				¬


				3	3	8
4 3 1		2	0	3	3	8

							.
				2	4	5
2 1 3		0	0	2	4	5


					7
8 7 3		7®	0 5		7	13®

ɉɪɢɛɚɜɥɹɟɦ ɤ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ ɜɬɨɪɭɸ

2 3	1 5			2 3	1 5
			¬				¬

		8				8
0 3 3		8		0 3 3		8

							.
		5
0 2 4		5		0 5 7		13



0 5 7		13®		0 5 7		13®

ɉɪɢɛɚɜɥɹɟɦ ɤ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ ɜɬɨɪɭɸ ɭɦɧɨɠɟɧɧɭɸ ɧɚ í5/3 ɤ ɱɟɬɜɟɪɬɨɣ ɫɬɪɨɤɟ ɬɪɟɬɶɸ ɭɦɧɨɠɟɧɧɭɸ ɧɚ í1:

2 3	1 5			2 3	1 5
			¬				¬

		8				8
0 3 3		8		0 3 3		8

							.
					2
0 5 7		13		0 0	2	1 / 3


					0	0
0 5 7		13®		0 0	0	0	®

Ȼɚɡɢɫɧɵɣ ɦɢɧɨɪ

2 3 1

0 3 3 12 v0.

0 0 2

Ɉɩɪɟɞɟɥɢɬɟɥɶ ɜɫɟɣ ɦɚɬɪɢɰɵ ɪɚɜɟɧ ɧɭɥɸ ɬ ɤ ɫɨɞɟɪɠɢɬ ɧɭɥɟɜɭɸ ɫɬɪɨɤɭ ɋɥɟɞɨɜɚɬɟɥɶɧɨ rangA 3.

<<< < Предыдущая 1 2 3 4 5 6 7 89 / 129 10 11 12 > Следующая >>>

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]