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Cálculo Matricial: Ejemplo de Cálculo de Matrices y Determinantes - Prof. 5364, Apuntes de Matemáticas

Este documento contiene un ejemplo de cómo calcular la matriz inversa, el determinante y realizar operaciones básicas con matrices utilizando el paquete maple. Se muestra el cálculo de la matriz a, su transpuesta at, el determinante det(a), la matriz inversa a1 y la multiplicación a*a1.

Tipo: Apuntes

2015/2016

Subido el 25/01/2016

karimabm
karimabm 🇪🇸

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reset()
use (linalg);use(plot);use(matrix);
Warning: Identifier 'htranspose' already has a value. It is not exported. [use]
Warning: Identifier 'transpose' already has a value. It is not exported. [use]
Warning: Identifier 'Pyramid' seems to be protected. It is not exported. [use]
Warning: Identifier 'hull' already has a value. It is not exported. [use]
Warning: Identifier 'Integral' seems to be protected. It is not exported. [use]
Warning: Identifier 'subs' already has a value. It is not exported. [use]
Warning: Identifier 'subsex' already has a value. It is not exported. [use]
Warning: Identifier 'info' already has a value. It is not exported. [use]
A:=randomMatrix(10,10,Unimodular);
8-2 1 5 3 -17340
8-7-4 0 -318232
-6-3-4-5-1090224
-85151-2 0 7 7 -2
-10 9 10 9 9 -5-7-3 2 -8
-5-2 7 8 -1 3 1 -5 9 -7
9 2 -9-6 5 -8 3 9 -9 7
-5-5-6 0 2 -8 3 -1-3-5
4363-3 10 1 3 7 4
-2-4-10 -8-4-1 2 3 -6 3
AT:=transpose(A);
8 8 -6-8-10 -5 9 -5 4 -2
-2-7-3 5 9 -2 2 -5 3 -4
1-4-4 1 10 7 -9-6 6 -10
5 0 -5 5 9 8 -6 0 3 -8
3-3-10 1 9 -1 5 2 -3-4
-1 1 9 -2-5 3 -8-8 10 -1
7 8 0 0 -7 1 3 3 1 2
3 2 2 7 -3-5 9 -1 3 3
432729-9-3 7 -6
0 2 4 -2-8-7 7 -5 4 3
det(A)
1
A1:=inverse(A);
-57 -62 -14 -7-62 64 60 85 72 -55
597 699 114 90 672 -782 -711 -869 -729 592
-242 -265 -40 -40 -255 328 295 329 281 -226
261 317 45 42 300 -363 -326 -377 -315 262
-305 -388 -58 -46 -367 414 375 463 382 -320
-118 -148 -26 -16 -142 149 137 184 152 -124
452 531 92 65 513 -576 -527 -669 -560 452
-489 -557 -95 -73 -539 630 574 704 594 -476
-78 -114 -14 -12 -105 115 103 126 101 -90
233 261 49 33 255 -289 -265 -338 -286 225
A*A1;
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reset() use (linalg);use(plot);use(matrix); Warning: Identifier 'htranspose' already has a value. It is not exported. [use] Warning: Identifier 'transpose' already has a value. It is not exported. [use] Warning: Identifier 'Pyramid' seems to be protected. It is not exported. [use] Warning: Identifier 'hull' already has a value. It is not exported. [use] Warning: Identifier 'Integral' seems to be protected. It is not exported. [use] Warning: Identifier 'subs' already has a value. It is not exported. [use] Warning: Identifier 'subsex' already has a value. It is not exported. [use] Warning: Identifier 'info' already has a value. It is not exported. [use] A:=randomMatrix(10,10,Unimodular);

  • 6 - 3 - 4 - 5 - 10 9 0 2 2 4
  • 8 5 1 5 1 - 2 0 7 7 - 2
  • 10 9 10 9 9 - 5 - 7 - 3 2 - 8
  • 5 - 2 7 8 - 1 3 1 - 5 9 - 7
  • 5 - 5 - 6 0 2 - 8 3 - 1 - 3 - 5
  • 2 - 4 - 10 - 8 - 4 - 1 2 3 - 6 3

AT:=transpose(A);

  • 2 - 7 - 3 5 9 - 2 2 - 5 3 - 4
  • 1 1 9 - 2 - 5 3 - 8 - 8 10 - 1

det(A) 1 A1:=inverse(A);

  • 57 - 62 - 14 - 7 - 62 64 60 85 72 - 55
  • 242 - 265 - 40 - 40 - 255 328 295 329 281 - 226
  • 305 - 388 - 58 - 46 - 367 414 375 463 382 - 320
    • 118 - 148 - 26 - 16 - 142 149 137 184 152 - 124
  • 489 - 557 - 95 - 73 - 539 630 574 704 594 - 476
    • 78 - 114 - 14 - 12 - 105 115 103 126 101 - 90

A*A1;

A*A1;

rank(A); 10 delete a; solve([2y-z=a,3x-2z=11,y+z=6,2x+y-4*z=a],[x,y,z]);

x = 5 , y = 4 , z = 2  if a = 6

Æ if a ¹ 6

M:=expr2Matrix([2y-z=a,3x-2z=11,y+z=6,2x+y-4*z=a],[x,y,z]);

0 2 - 1 a

2 1 - 4 a

A:=submatrix(M,1..4,1..3);

a:=6;rank(M);rank(A); 6 3 3 a:=4;rank(M);rank(A); 4 4 3 A:=matrix([[0,6,36,216],[0,0,6,36],[0,0,0,6],[0,0,0,0]]);

A^2; A^3; A^4; A^5;