1

LI GII MT S BI TP

TON CAO CP 2

Li gii mt s bi tp trong ti liu ny dng tham kho. C mt s bi tp do mt s

sinh vin gii. Khi hc, sinh vin cn la chn nhng phng php ph hp v n gin

hn. Chc anh ch em sinh vin hc tp tt

2

BI TP V HNG CA MA TRN

Bi 1:

Tnh hng ca ma trn:

1)

A

2 4 3 1 01 2 1 4 20 1 1 3 11 7 4 4 5

h1 h2

1 2 1 4 22 4 3 1 00 1 1 3 11 7 4 4 5

h1(2)h2h1(1)h4

1 2 1 4 20 0 1 9 40 1 1 3 10 5 3 0 3

h2h3

1 2 1 4 20 1 1 3 10 0 1 9 40 5 3 0 3

h2(5)h4

1 2 1 4 20 1 1 3 10 0 1 9 40 0 2 15 8

h3(2)h4

1 2 1 4 20 1 1 3 10 0 1 9 40 0 0 33 0

r A 4

2)

3

A

0 2 41 4 53 1 70 5 102 3 0

h1h2

1 4 50 2 43 1 70 5 102 3 0

h1 3 h3h1 2 h4

1 4 50 2 40 11 220 5 100 5 10

h2 12

1 4 50 1 20 11 220 5 100 5 10

h2 11 h3h2 5 h4h2 5 h5

1 4 50 1 20 0 00 0 00 0 0

r A 2

2)

A 2 1 3 2 44 2 5 1 72 1 1 8 2

h1(-2)h2h1(-1)h3

2 1 3 2 40 0 1 5 10 0 2 10 2

h2(-2)h3 2 1 3 2 40 0 1 5 10 0 0 0 0

r A 2

3)

A

1 3 5 12 1 5 45 1 1 77 7 9 1

h1 2 h2h1 5 h3h1 7 h4

1 3 5 10 7 15 60 14 24 120 14 26 6

h2 2 h3h2 2 h4

1 3 5 10 7 15 60 0 6 00 0 4 6

h3 16

1 3 5 10 7 15 60 0 1 00 0 4 6

h4 4 h4

1 3 5 10 7 15 60 0 1 00 0 0 6

r A 4

4

4)

A

3 1 3 2 55 3 2 3 41 3 5 0 77 5 1 4 1

h1 h3

1 3 5 0 75 3 2 3 43 1 3 2 57 5 1 4 1

h1 5 h2h1 3 h3h1 7 h4

1 3 5 0 70 12 27 3 310 8 18 2 160 16 36 4 48

h312

h2

1 3 5 0 70 4 9 1 80 12 27 3 310 16 36 4 48

h2 3 h3h2 4 h4

1 3 5 0 70 4 9 1 80 0 0 0 70 0 0 0 16

h3 167

h4

1 3 5 0 70 4 9 1 80 0 0 0 70 0 0 0 0

r A 3

5)

A

2 2 1 5 11 0 4 2 12 1 5 2 11 2 2 6 13 1 8 1 11 2 3 7 2

h1h2

1 0 4 2 12 2 1 5 12 1 5 2 11 2 2 6 13 1 8 1 11 2 3 7 2

h1(2)h2h1(2)h3h1h4h1(3)h5h1(1)h6

1 0 4 2 10 2 7 9 30 1 3 2 10 2 6 8 20 1 4 5 20 2 7 9 3

h2h3

1 0 4 2 10 1 3 2 10 2 7 9 30 2 6 8 20 1 4 5 20 2 7 9 3

h2(2)h3h2(2)h4h2h5h2(2)h6

1 0 4 2 10 1 3 2 10 0 1 3 10 0 0 4 00 0 1 3 10 0 1 3 1

h3h5h3(1)h6

1 0 4 2 10 1 3 2 10 0 1 3 10 0 0 4 00 0 0 0 00 0 0 0 0

r A 4

5

6)

A

1 1 2 3 42 1 1 2 01 2 1 1 31 5 8 5 123 7 8 9 13

h1(2)h2h1h3h1(1)h4h1(3)h5

1 1 2 3 40 3 5 4 80 1 1 3 70 6 10 8 160 4 2 0 1

h2h3

1 1 2 3 40 1 1 3 70 3 5 4 80 6 10 8 160 4 2 0 1

h2(3)h3h2(6)h4h2(4)h5

1 1 2 3 40 1 1 3 70 0 8 13 290 0 16 26 580 0 6 12 29

h3(1)h4h3h5

1 1 2 3 40 1 1 3 70 0 8 13 290 0 0 0 00 0 2 1 0

h5(4)h3

1 1 2 3 40 1 1 3 70 0 0 9 290 0 0 0 00 0 2 1 0

h5h4h3

1 1 2 3 40 1 1 3 70 0 2 1 00 0 0 9 290 0 0 0 0

r( A) 4

8

- Nu 0 th r(A) = 4

2)

A

3 1 1 4 4 10 11 7 17 32 2 4 3

h2 h4

3 1 1 42 2 4 31 7 17 3 4 10 1

c1 c4

4 1 1 33 2 4 23 7 17 11 4 10

c1c2

1 4 1 32 3 4 27 3 17 14 1 10

h1 2 h2h1 7 h3h1 4 h4

1 4 1 30 5 2 40 25 10 200 15 6 12

h2 5 h3h2 3 h4

1 4 1 30 5 2 40 0 0 00 0 0

h3 h4

1 4 1 30 5 2 40 0 0 0 0 0 0

Vy:

- Nu = 0 th r(A) = 2

- Nu 0 th r(A) = 3

3)

A

4 1 3 30 6 10 21 4 7 26 8 2

C2C4

4 3 3 10 2 10 61 2 7 46 2 8

h1 h3

1 2 7 40 2 10 64 3 3 16 2 8

9

h1 4 h3h1 6 h4

1 2 7 40 2 10 60 5 25 150 10 50 24

h212

1 2 7 40 1 5 30 5 25 150 10 50 24

h2 5 h3h2 10 h4

1 2 7 40 1 5 30 0 0 00 0 0 6

h3 h4

1 2 7 40 1 5 30 0 0 60 0 0 0

Vy:

- Khi 6 0 6 th r(A) = 2

- Khi 6 0 6 th r(A) = 3

4)

A

3 9 14 10 6 10 21 4 7 23 1 2

C2C4

3 1 14 90 2 10 61 2 7 43 2 1

h1 h3

1 2 7 40 2 10 63 1 14 93 2 1

h1 3 h3h1 3 h4

1 2 7 40 2 10 60 7 35 210 4 20 12

h212

1 2 7 40 1 5 30 7 35 210 4 20 12

h2 7 h3h2 4 h4

1 2 7 40 1 5 30 0 0 00 0 0

h3 h4

1 2 7 40 1 5 30 0 0 0 0 0 0

Vy :

- Nu = 0 th r(A) = 2

- Nu 0 th r(A) = 3