Matrices 2x2 3x3 4x4 5x5

70
8 -2 0 100 -2 10 -4 -200 0 -4 8 0 A= B= C= D1= D2= D3=

Transcript of Matrices 2x2 3x3 4x4 5x5

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8 -2 0 100

-2 10 -4 -200

0 -4 8 0

A=

B=

C=

D1=

D2=

D3=

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6.66666667

-23.3333333

-11.6666667

100

-200

0

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matriz orig

15 0 110 0

0 110 0 1958

110 0 1958 0

0 1958 0 41030

1958 0 41030 0

0 41030 0 925958

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0 110 0 1958

0 0 1151.3333333333 0

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matriz 21 0 7.3333333333 0

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0 0 0 0

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  inal

1958 0 220

0 41030 0

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1 0 0 ! "6=

0 249599.999999998 0

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0 0 2 ! "4=0 0 0 ! "5=

1 0 0 ! "6=

0 1 0 ! "7=

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220

0

220

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3916

220

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82060 7 1 2 2

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# #1

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3 -3 18 14.6666667

4 -2 8 14.6666667

5 -1 2 14.66666676 0 0 14.6666667

7 1 2 14.6666667

8 2 8 14.6666667

9 3 18 14.6666667

10 4 32 14.6666667

11 5 50 14.6666667

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 #4="2%"3%"4&2%"5&3%

 #5="2%"3%"4&2%"5&3%"6

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&2# &3# &4# &5# &2 &3

1250 -6250 31250 -156250 25 -125

512 -2048 8192 -32768 16 -64

162 -486 1458 -4374 9 -27

32 -64 128 -256 4 -8

2 -2 2 -2 1 -1

0 0 0 0 0 0

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&4 &5 &6 &7

625 -3125 15625 -78125

256 -1024 4096 -16384

81 -243 729 -2187

16 -32 64 -128

1 -1 1 -1

0 0 0 0

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1 1 1 1

16 32 64 128

81 243 729 2187

256 1024 4096 16384

625 3125 15625 78125

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

1958 0 41030 0

'3 '4 '5 ('&2)1

0 0 0 1248.444444444

0 0 0 300.4444444444

0 0 0 11.1111111111

0 0 0 44.4444444444

0 0 0 160.44444444440 0 0 215.1111111111

0 0 0 160.4444444444

0 0 0 44.4444444444

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0 0 0 300.4444444444

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0 0 0 215.1111111111

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0 0 0 215.1111111111

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$

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&8 &9 &10

390625 -1953125 9765625

65536 -262144 1048576

6561 -19683 59049

256 -512 1024

1 -1 1

0 0 0

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1 1 1

256 512 1024

6561 19683 59049

65536 262144 1048576

390625 1953125 9765625

0 0 0

0 0 00 0 0

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('&2)2 ('&2)3 ('&2)4 ('&5)5

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7 28 140

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matri

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 original

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0 0

0 0

0 0

0 0

0 0

0 0

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*D+,0 *D+,0 ! /3= *D+,0

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*D+,0 *D+,0 ! /5= *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0 ! /2= *D+,0

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*D+,0 *D+,0 ! /4= *D+,0

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*D+,0 *D+,0 ! /6= *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

*D+,0 *D+,0 ! /2= *D+,0

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*D+,0 *D+,0 ! /4= *D+,0

*D+,0 *D+,0 ! /5= *D+,0

*D+,0 *D+,0 ! /6= *D+,0

*D+,0 *D+,0 ! /7= *D+,0

*D+,0 *D+,0

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*D+,0 *D+,0 ! /2= *D+,0

*D+,0 *D+,0 ! /3= *D+,0

*D+,0 *D+,0 ! /4= *D+,0

*D+,0 *D+,0 ! /5= *D+,0

*D+,0 *D+,0 ! /6= *D+,0*D+,0 *D+,0 ! /7= *D+,0

*D+,0 *D+,0 ! /8= *D+,0

*D+,0 *D+,0

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*D+,0 *D+,0 ! /5= *D+,0

*D+,0 *D+,0 ! /6= *D+,0

*D+,0 *D+,0 ! /7= *D+,0

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*D+,0 *D+,0

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*D+,0 *D+,0 ! /8= *D+,0

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*D+,0 *D+,0 ! /10= *D+,0

*D+,0 *D+,0

*D+,0 *D+,0

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*D+,0 *D+,0 ! /6= *D+,0

*D+,0 *D+,0 ! /7= *D+,0

*D+,0 *D+,0 ! /8= *D+,0

*D+,0 *D+,0 ! /9= *D+,0

*D+,0 *D+,0 ! /10= *D+,0

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*D+,0 *D+,0 ! /12= *D+,0

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# # &2#

1 1 4 4 4

2 2 7 14 28

3 3 9 27 81

4 4 10 40 160

5 5 9 45 2256 6 7 42 252

7 7 4 28 196

8 0 0 0 0

9 0 0 0 0

10 0 0 0 0

11 0 0 0 0

12 0 0 0 0

13 0 0 0 0

14 0 0 0 0

15 0 0 0 0$ 28 50 200 946

= 7

# #1 #2

1 1 4 7.1428571429 3.9285714286

2 2 7 7.1428571429 7.1428571429

3 3 9 7.1428571429 9.0714285714

4 4 10 7.1428571429 9.7142857143

5 5 9 7.1428571429 9.0714285714

6 6 7 7.1428571429 7.1428571429

7 7 4 7.1428571429 3.9285714286

8 0 0 7.1428571429 -0.5714285714

9 0 0 7.1428571429 -0.5714285714

10 0 0 7.1428571429 -0.5714285714

11 0 0 7.1428571429 -0.5714285714

12 0 0 7.1428571429 -0.5714285714

13 0 0 7.1428571429 -0.5714285714

14 0 0 7.1428571429 -0.5714285714

15 0 0 7.1428571429 -0.5714285714

 #1=/2%/3

 #2=/2%/3%/4&2

 #3=/2%/3%/4&2%/5

 #4=/2%/3%/4&2%/5&3%

 #5=/2%/3%/4&2%/5&3%/6

 #6=/2%/3%/4&2%/5&3%/6&4%

 #7=/2%/3%/4&2%/5&3%/6&4%/7

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 #8=/2%/3%/4&2%/5&3%/6&4%/7&5%

 #9=/2%/3%/4&2%/5&3%/6&4%/7&5%/8&

 #10=/2%/3%/4&4%/5&3%/6&4%/7&5%/8&6%/

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&3# &4# &5# &6#

4 4 4 4

56 112 224 448

243 729 2187 6561

640 2560 10240 40960

1125 5625 28125 1406251512 9072 54432 326592

1372 9604 67228 470596

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 04952 27706 162440 985786

 #3 #4 #5 #6

*D+,0 *D+,0 *D+,0 *D+,0

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&3

/6&4

&4%/7&5

/7&5%/8&6

&5%/8&6%/9&7

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8&6%/9&7%/10&8

6%/9&7%/10&8%/11&9

&7%/10&8%/11&9%/12&10

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&7# &8# &9# &10#

4 4 4 4

896 1792 3584 7168

19683 59049 177147 531441

163840 655360 2621440 10485760

703125 3515625 17578125 878906251959552 11757312 70543872 423263232

3294172 23059204 161414428 1129900996

0 0 0 0

0 0 0 0

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 #7 #8 #9 #10

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&2 &3 &4 &5

1 1 1 1

4 8 16 32

9 27 81 243

16 64 256 1024

25 125 625 312536 216 1296 7776

49 343 2401 16807

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'1 '2 '3 '4

-3.1428571429 0.0714285714 *D+,0 *D+,0

-0.1428571429 -0.1428571429 *D+,0 *D+,0

1.8571428571 -0.0714285714 *D+,0 *D+,0

2.8571428571 0.2857142857 *D+,0 *D+,0

1.8571428571 -0.0714285714 *D+,0 *D+,0

-0.1428571429 -0.1428571429 *D+,0 *D+,0

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-7.1428571429 0.5714285714 *D+,0 *D+,0

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 ala e alore

&6 &7 &8

1 1 1

64 128 256

729 2187 6561

4096 16384 65536

15625 78125 39062546656 279936 1679616

117649 823543 5764801

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0 0 0

0 0 0

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'5 '6 '7

*D+,0 *D+,0 *D+,0

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&9 &10 &11

1 1 1

512 1024 2048

19683 59049 177147

262144 1048576 4194304

1953125 9765625 4882812510077696 60466176 362797056

40353607 282475249 1977326743

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$1

$2

$3

$4

$5

$6

$7

$8

$9

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$10

$11

$12

$13

$14

$15

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&12 &13 &14

1 1 1

4096 8192 16384

531441 1594323 4782969

16777216 67108864 268435456

244140625 1220703125 61035156252176782336 13060694016 78364164096

13841287201 96889010407 678223072849

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('&2)1 ('&2)2 ('&2)3

9.8775510204 0.0051020408 *D+,0

0.0204081633 0.0204081633 *D+,0

3.4489795918 0.0051020408 *D+,0

8.1632653061 0.0816326531 *D+,0

3.4489795918 0.0051020408 *D+,0

0.0204081633 0.0204081633 *D+,0

9.8775510204 0.0051020408 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

51.0204081633 0.3265306122 *D+,0

9.8775510204 0.0051020408 *D+,0

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24.9795918367 0.137755102 *D+,0

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187.9183673469 1.1224489796 *D+,0

238.9387755102 1.4489795918 *D+,0

289.9591836735 1.7755102041 *D+,0

340.9795918367 2.1020408163 *D+,0

392 2.4285714286 *D+,0

443.0204081633 2.7551020408 *D+,0

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&15 &16 &17

1 1 1

32768 65536 131072

14348907 43046721 129140163

1073741824 4294967296 17179869184

30517578125 152587890625 762939453125470184984576 2821109907456 16926659444736

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*D+,0 *D+,0 *D+,0

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&18 &19 &20

1 1 1

262144 524288 1048576

387420489 1162261467 3486784401

68719476736 274877906944 1099511627776

3814697265625 19073486328125 95367431640625101559956668416 609359740010496 3656158440062980

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