puteri de matrici

14
Prof. Marcela V. Mihai Colegiul Tehnic “Gheorghe Asachi”, Bucuresti

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Page 1: Puteri de matrici

Prof. Marcela V. MihaiColegiul Tehnic “Gheorghe

Asachi”, Bucuresti

Page 2: Puteri de matrici

101

010

101

202

010

202

22

22

202

010

202

404

010

404

33

33

202

010

202

808

010

808

Page 3: Puteri de matrici

11

11

202

010

202

nn

nn

nn

nn

nn

nn

202

010

202

22022

010

22022

11

11

Page 4: Puteri de matrici

31

13A

,

2

3

2

12

1

2

3

2

A .

6cos

6sin

6sin

6cos

2

A

6cos

6sin

6sin

6cos

2

nn

nnA nn

Page 5: Puteri de matrici

n

k

kknkn

nn YXCYXA0

)(

Page 6: Puteri de matrici

100

310

211

A

000

300

210

B

000

000

3002B 3p

100

3102

)13(1

100

3102

3341

100

3102

)1(321

000

000

300

2

)1(

000

300

210

100

010

001

)( 22133

n

nnn

n

nnn

n

nnnn

nnn

BCBCIBIA nnnn

Page 7: Puteri de matrici
Page 8: Puteri de matrici

ab

baA

nn

nnn

ab

baA

11

111

nn

nn

nnnn

nnnnnn

ab

ba

bbaabaab

baabbbaaAAA

,1

1

nnn

nnn

baabb

bbaaa .)(

)(1

11

111

nnn

nnn

baba

baba

.

2

)()(

2

)()(2

)()(

2

)()(

nnnn

nnnn

n

babababa

babababa

A

Page 9: Puteri de matrici

100

110

011

A

100

410

641

,

100

310

331

,

100

210

1214232 AAAAAAA

.

100

10

1

n

an

An

n

100

110

11

n

ann

An

Page 10: Puteri de matrici

1),-(n2)-(n21a n 2

)1( nnan

100

102

)1(1

n

nnn

An

2

1

12...21

1

2

2

1

0

1

21

23

12

1

nna

nna

ana

ana

aa

aa

a

n

n

nn

nn

1,1 nana nn

Page 11: Puteri de matrici

2Mdc

baA

cuAATr ,0)det()(2

2,1

,

,,

,

211

1

2121

21

pentrun

pentrux

n

nn

n

222 )det()( OIAAATrA

nIxAAxA nn

n ,)det( 21

n

.)( 1 AATrA nn

Page 12: Puteri de matrici

41

21A

0652 21

.2332

32 nnnn

nx

10

01236

41

2123 11 nnnnnA

,32230

03223

23432

232232

1

nn

nn

nnnn

nnnnnA .

23232

23232 11

nnnn

nnnnnA

.32

624(A)det , 541Tr(A)

Page 13: Puteri de matrici

13

35A 0442

.221

.10

01214

13

352 21

nnn nnA

.2)1(223

232)1(2511

11

nnn

nnnn

nnn

nnnA

,36

12

A

.36

1255 11

nnn AA

0.6-6det(A) si 5Tr(A)

12,4Adet nn nx

Page 14: Puteri de matrici