Тема 2.6. Ранг матрицы. Исследование и решение СЛАУ методом Гаусса

x1 + x2 + x3 = 3,

− x2

− x3 = − 1,

x1

1.

− x2

− x3 = 1,

x1

- x

1

−

x

2

+

x

3

=

− 1,

- x

x

x

− 1.

1

+

2

−

3

=

5x1 −

3x2 +

2x3 +

4x4 =

3,

4x1 −

2x2 +

3x3 +

7x4 =

1,

3.

8x1 − 6x2 − x3 − 5x4 = 9,

7x1 −

3x2 +

7x3 + 17x4 = 10.

8x1 +

6x2 +

5x3 +

2x4 = 21,

3x1 +

3x2 +

2x3 +

x4 =

10,

5.

4x1 +

2x2 +

3x3 +

x4 =

8,

3x

1

+

5x

2

+

x

3

+

x

4

=

15,

= 18.

7x

1

+

4x

2

+

5x

3

+

2x

4

2x1 +

5x2 −

8x3 =

8,

4x1 +

3x2 −

9x3 =

9,

7.

2x1 +

3x2 −

5x3 =

7,

x1 +

8x2 −

7x3 =

12.

5x1 −

3x2 +

2x3 +

4x4 =

3,

4x1 −

2x2 +

3x3 +

7x4 =

1,

9.

8x1 − 6x2 − x3 − 5x4 = 9,

7x1 −

3x2 +

7x3 + 17x4 = 10.

x1 + 2x2 − 3x3 = − 4,

x1

+

x2 + x3 = 4,

11.

2x1

− x2 + x3 = 6,

5x1 + 4x2 − 4x3 =

2.

2x1 + 5x2 + x3 + 3x4 = 2,

4x1 +

6x2 +

3x3 +

5x4 =

4,

2.

4x1 +

14x2 +

x3 +

7x4 =

4,

2x1 − 3x2 + 3x3 + x4 = 7.

2x1 − x2 + x3 + 2x4 + x5 = 2,

6x1 −

3x2 +

2x3 +

4x4 +

5x5 =

3,

4.

6x1 −

3x2 +

4x3 +

8x4 +

13x5 =

9,

4x1 − 2x2 + x3 + x4 + 2x5 = 1.

3x1 +

2x2 +

2x3 +

2x4 =

2,

2x1 +

3x2 +

2x3 +

5x4 =

3,

6.

9x1 +

x2 +

4x3 −

5x4 =

1,

2x

1

+

2x

2

+

3x

3

+

4x

4

=

5,

7x

x

6x

x

7.

1

+

2

+

3

−

4

=

x1 − x 2 − 2x3 = − 2,

x1 + x 2 − 7x3 = − 5,

8.

2x1 − x 2 − 2x3 = − 1,

3x1 − x 2 − 5x 3 = 3.

x1 + x2 − 3x4 = 1,

x1 −

x2 + 2x3 − x4 = 0,

10.

4x1

−

2x2 +

6x3 +

3x4 =

4,

2x1

+

4x2 −

2x3 +

4x4 =

7.

2x1 + 2x2 + x3 = − 5,

3x1

−

4x2 −

5x3 =

6,

12.

x1 + 3x2 + 4x3 = − 8,

6x1

+

x2 =

− 7.

2x1 + x2 − x3 − 3x4 = 4,

2x1 − x2 + x3 + x4 = 1,

13.

5x1 + x2 − x3 − 2x4 = 3,

5x1 − x2 − x3 + 2x4 = − 1.

2x1 + 2x2 + 2x3 − x4 = 1,

5x1 +

5x2 +

2x3 =

2,

15.

2x1

+

3x2

+

x3

+

x4 =

1,

2x

1

+

2x

2

+

2x

3

−

x

4

=

1,

7x

7x

4x

x

3.

1

+

2

+

3

−

4

=

2x1 − x2 + x3 = − 2,

x1 + 2x2 + 3x3 = − 1,

17.

3x2 −

2x3 =

3,

x1 −

2x

1

−

x

2

+

x

3

=

0,

3x

x

3.

1

+

2

+

4x

3

=

−

x1 + x2 + 3x3 − 2x4 = 3,

2x1 −

3x2 −

2x3 −

3x4 =

7,

19.

3x1 − x2 − x3 + 2x4 = − 1,

2x1 − 5x2 + 2x3 + x4 = − 7.

x1 − 2x2 − 4x3 + 3x4 = 4,

x2 + x3 − x4 = − 3,

21.

x1 + 3x2 − 3x3 = 1,

x1 −

7x2 +

x3 +

3x4 =

− 11.

− 4x1 − 2x2 + 3x3 + x4 = 4,

x1 + x2 − x3 = − 3,

23.

− 3x1 + 3x2 + x4 = 1,

x1 − 7x2 + 3x3 = − 3.

− x1 +

x3 =

0,

3x1 + 2x2 + x3 − x4 = 1,

14.

2x1

+

3x2

+

x3 +

x4 =

1,

4x

1

+

5x

2

+

3x

3

=

1,

5x

5x

2x

2.

1

+

2

+

3

=

2x1 + x2 + 3x3 − x4 = 1,

2x1 + 3x2 + x3 − x4 = 1,

16.

5x1 +

5x2 +

2x3 =

2,

2x

1

+

2x

2

+

2x

3

−

x

4

=

1,

5x

5x

2x

1

+

2

+

3

=

2.

3x1 + x2 + 4x3 = − 3,

x1 + 2x2 + 3x3 = − 1,

18.

x1 − 3x2 − 2x3 = 3,

2x1 − x2 + x3 = 2.

x1 + 2x2 + 3x3 = 5,

x1 + 3x2 − x3 = 2,

20.

2x1 + x2 + 4x3 = 5,

2x1 + x2 + 3x3 = 4.

2x1 −

2x2 +

3x3 −

4x4 =

12,

x1 + x2 − x3 + x4 = 5,

22.

2x1 +

3x2 −

3x4 =

9,

x1 − 7x2 + 3x3 + x4 = 5.

x1 + x2 + 3x3 = 5,

2x1 + x2 + 2x3 = 5,

24.

x1 +

3x2 +

6x3 =

10,

x1 + 3x2 + 3x3 = 7.