Práctica 2 de fonaments matematics (2016)

Pràctica Español
Universidad Universidad Autónoma de Barcelona (UAB)
Grado Nanociencia y Nanotecnología - 1º curso
Asignatura Fonaments Matematics
Profesor K.
Año del apunte 2016
Páginas 10
Fecha de subida 25/10/2017
Descargas 0
Subido por

Descripción

Práctica de fundamentos matemáticos

Vista previa del texto

practica2mates (1).wxmx 1 / 10 PRÁCTICA 2 (FUNDAMENTOS MATEMÁTICOS) practica2mates (1).wxmx Adolfo de Hoyos-Limón (1459425) Maider Isasmendi (1459 EJERCICIO 1 Base imagen: matrix([0,0,0,0,0],[1,0,0,0,0],[0,1,0,0,0], [0,0,1,0,0],[0,0,2,1,0],[0,0,0,0,1]) Base del nucleo: matrix([1],[0],[0],[0],[0],[0]) EJERCICIO 2 Base preimagen: matrix([1,0,0,0],[0,1,0,0], [0,-1,1,0],[0,0,0,1],[0,0,0,0],[0,0,0,-2]) Base imagen: Ejercicio 3 a)1:(lambda-2)*(lambda+1) [lambda=-1,lambda=2] 2:(lambda-4)*(lambda-2)*(lambda-1)*lambda*(lambda+1)* (lambda+2) [lambda=-2,lambda=-1,lambda=0,lambda=1,lambda=2, lambda=4] EJERCICIO 4 a)[[[2,-1],[1,1]],[[[1,1]],[[1,-2]]]] b)[[[-2,4,1,2,-1,0],[1,1,1,1,1,1]],[[[0,0,0,1,-4,4]], [[0,0,0,1,2,1]],[[0,0,0,1,-1,-2]],[[0,1,1,0,0,0]], [[0,1,-2,0,0,0]],[[1,0,0,0,0,0]]]] EJERCICIO 5 a)1):-(lambda-2)^2*(lambda-1)^2*lambda*(lambda+1)^2 2):[[2,-1,1,0],[2,2,2,1]] b)[[[2,-1,1,0],[2,2,2,1]],[[[0,1,0,0,1,0,2],[0, 0,0,1,1,1,2]],[[0,1,0,-3,-1,-2,-3],[0,0,1,-1,-1,0,1]],[[1,0,0,-3,-2,-2,-4],[0,1,-1,-1,0,-1,-1]],[[1,1,1,-2,-2,-1,-5]]]] c) 7 valores vectores propios, 4 valores propios, 3 de multiplicidad 2 y 1 de multiplicidad 1, 6+1=7 d) 1):matrix([0,1,0,0,1,0,2],[0,0,0,1,1,1,2], [0,1,0,-3,-1,-2,-3],[0,0,1,-1,-1,0,-1], [1,0,0,-3,-2,-2,-4],[0,1,-1,-1,0,-1,-1], [1,-1,1,-2,-2,-1,-5]) 2):matrix([1/2],[2^n-(-1)^n+1/2],[-1/2],[3*(-1)^n-2], [2^n+(-1)^n-1],[2*(-1)^n-3/2],[2^(n+1)+3*(-1)^n-5/2]) 2 / 10 practica2mates (1).wxmx 3 / 10 (%i85) M:matrix([1,1],[2,0]); (%o85) 1 1 2 0 (%i86) V=[a1x+a2y,a1,a2]; (%o86) V = [ a2y + a1x , a1 , a2 ] (%i87) M:matrix([0,0,0,0,0,0],[0,1,1,0,0,0],[0,2,0,0,0,0],[0,0,0,2,1,0],[0,0 0 0 0 0 0 0 0 1 1 0 0 0 (%o87) 0 2 0 0 0 0 0 0 0 2 1 0 0 0 0 4 1 2 0 0 0 0 2 0 practica2mates (1).wxmx 4 / 10 (%i88) N:addrow(M,ident(6));P:transpose(echelon(transpose(N))); 0 0 0 0 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 2 1 0 0 0 0 4 1 2 (%o88) 0 0 0 0 2 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 (%o89) 0 1 0 0 0 0 0 0 0 0 2 1 - 1 2 1 0 0 0 0 0 0 0 0 0 2 0 - 1 4 1 2 1 1 2 4 0 0 0 practica2mates (1).wxmx 5 / 10 (%i90) Baseimatge:submatrix(7,8,9,10,11,12,P,6);Basenucli:submatrix(1,2,3,4, 0 0 0 0 0 1 0 0 0 0 (%o90) 0 1 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 1 1 0 (%o91) 0 0 0 0 --> ejercicio 2 (%i92) M:matrix([0,0,0,0,0,0],[0,1,1,0,0,0],[0,2,0,0,0,0],[0,0,0,2,1,0],[0,0 0 0 0 0 0 0 0 1 1 0 0 0 (%o92) 0 2 0 0 0 0 0 0 0 2 1 0 0 0 0 4 1 2 0 0 0 0 2 0 (%i93) P:matrix([1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[0,0,0,0],[0,0,0,0]) 1 0 0 0 0 1 0 0 (%o93) 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 (%i94) S:addcol(M,P); 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 (%o94) 0 2 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 1 0 0 0 4 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 practica2mates (1).wxmx 6 / 10 (%i95) N:addrow(S,ident(10)); 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 1 0 0 0 4 1 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 (%o95) 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 (%i96) I:transpose(echelon(transpose(N))); (%o96) 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 1 2 1 2 - 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 -2 0 0 0 0 -2 0 0 0 1 0 - 1 2 0 practica2mates (1).wxmx 7 / 10 (%i97) submatrix(1,2,3,4,5,6,13,14,15,16,I,1,2,3,4,5,6); (%o97) 1 0 0 0 0 1 0 0 0 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 -2 (%i141) ejercicio 3; incorrect syntax: 3 is not an infix operator (%i99) M:matrix([1,1],[2,0]); (%o99) 1 1 2 0 (%i100) q:charpoly(M,lambda); (%o100) -( 1 - lambda )lambda - 2 (%i101) q:factor(q);solve(q,lambda);eigenvalues(M); (%o101) ( lambda - 2 )( lambda + 1 ) (%o102) [ lambda = - 1 , lambda = 2 ] (%o103) [ [ 2 , - 1 ] , [ 1 , 1 ] ] (%i104) A:matrix([0,0,0,0,0,0],[0,1,1,0,0,0],[0,2,0,0,0,0],[0,0,0,2,1,0],[0,0 0 0 0 0 0 0 0 1 1 0 0 0 (%o104) 0 2 0 0 0 0 0 0 0 2 1 0 0 0 0 4 1 2 0 0 0 0 2 0 (%i105) p:charpoly(A,lambda); (%o105) - lambda ( -( 1 - lambda )lambda (( 2 - lambda )( -( 1 - lambda )lambda - 4 )+ 4 lambda )- 2 (( 2 - lambda )( -( 1 - lambda )lambda - 4 )+ 4 lambda )) (%i106) p:factor(p); solve(p,lambda); eigenvalues(A); (%o106) ( lambda - 4 )( lambda - 2 )( lambda - 1 )lambda( lambda + 1 )( lambda + 2 ) (%o107) [ lambda = - 2 , lambda = - 1 , lambda = 0 , lambda = 1 , lambda = 2 , lambda = 4 ] (%o108) [ [ - 2 , 4 , 1 , 2 , - 1 , 0 ] , [ 1 , 1 , 1 , 1 , 1 , 1 ] ] --> ejercicio 4 practica2mates (1).wxmx 8 / 10 (%i109) M:matrix([1,1],[2,0]); (%o109) 1 1 2 0 (%i110) eigenvectors(M); (%o110) [ [ [ 2 , - 1 ] , [ 1 , 1 ] ] , [ [ [ 1 , 1 ] ] , [ [ 1 , - 2 ] ] ] ] (%i111) A:matrix([0,0,0,0,0,0],[0,1,1,0,0,0],[0,2,0,0,0,0],[0,0,0,2,1,0],[0,0 0 0 0 0 0 0 0 1 1 0 0 0 (%o111) 0 2 0 0 0 0 0 0 0 2 1 0 0 0 0 4 1 2 0 0 0 0 2 0 (%i112) eigenvectors(A); (%o112) [ [ [ - 2 , 4 , 1 , 2 , - 1 , 0 ] , [ 1 , 1 , 1 , 1 , 1 , 1 ] ] , [ [ [ 0 , 0 , 0 , 1 , - 4 , 4 ] ] , [ [ 0,0,0,1,2,1]],[[0,0,0,1,-1,-2]],[[0,1,1,0,0,0]],[[0,1,-2,0, 0,0]],[[1,0,0,0,0,0]]]] (%i113) ejercicio 5; incorrect syntax: 5 is not an infix operator (%i154) X:matrix([1/2,-1/2,-1/2,-1/2,-1/2,0,1/2],[7/2,9/2,3/2,7/2,-3/2,-1,-1/ 1 2 1 2 - 1 2 - 1 2 7 9 3 7 2 2 2 2 5 1 2 2 -5 -4 (%o154) - 1 2 0 - 7 2 3 2 - 1 - 9 2 - 1 2 3 2 1 0 2 -1 - 1 2 1 3 2 2 0 -6 6 4 -1 1 -2 3 3 -1 11 11 2 2 3 - 11 17 2 2 4 - - 1 2 3 5 2 2 - - 1 -2 2 1 2 3 2 (%i149) factor(q:charpoly(X,lambda)); (%o149) 2 )2( 1 )2 -( lambda - lambda - lambda( lambda + 1 )2 (%i150) q:factor(q);solve(q,lambda);eigenvalues(X); (%o150) 2 )2( 1 )2 1 )2 -( lambda lambda lambda( lambda + (%o151) [ lambda = - 1 , lambda = 0 , lambda = 1 , lambda = 2 ] (%o152) [ [ 2 , - 1 , 1 , 0 ] , [ 2 , 2 , 2 , 1 ] ] practica2mates (1).wxmx 9 / 10 (%i145) eigenvectors(X); (%o145) [ [ [ 2 , - 1 , 1 , 0 ] , [ 2 , 2 , 2 , 1 ] ] , [ [ [ 0 , 1 , 0 , 0 , 1 , 0 , 2 ] , [ 0 , 0 , 0 , 1 , 1 , 1,2]],[[0,1,0,-3,-1,-2,-3],[0,0,1,-1,-1,0,-1]],[[1,0,0,-3,2,-2,-4],[0,1,-1,-1,0,-1,-1]],[[1,-1,1,-2,-2,-1,-5]]]] (%i158) Y:transpose(matrix([0,1,0,0,1,0,2],[0,0,0,1,1,1,2],[0,1,0,-3,-1,-2,-3 0 0 0 0 1 0 1 1 0 1 0 0 1 -1 0 0 0 1 0 -1 1 (%o158) 0 1 - 3 - 1 - 3 - 1 - 2 1 1 -1 -1 -2 0 1 -2 0 0 -2 -2 -1 -1 2 2 -3 -1 -4 -1 -5 (%i161) W:invert(Y).X.Y; 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 -1 (%o161) 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 (%i163) J:Y.W^n.Y^^-1; (%o163) 1 - 2 2 n -( - 1 )n + - 1 1 - 2 2 n -( - 1 )n + 2 1 ( - 1 )n - 2 3 3 1 2 2 2 ( - 1 )n - 2 n 2 n +( - 1 )n - 1 1 3 2 2 n + 1 + 3 ( - 1 )n - 5 2 2 ( - 1 )n + 1 2 1 2 2 n -( - 1 )n + - 1 1 3 2 1 1 2 2 2 2 - 2 n +( - 1 )n + 1 - 2 n - 2 n + 1 + 2 ( - 1 )n + 1 5 2 2 - 2 n + 1 + 3 ( - 1 )n + 1 0 2 ( - 1 )n - 2 - 2 n - 2 n + 1 + 3 ( - 1 )n + 1 1 - 2 n + 2 ( - 1 )n - - 2 2n - 2 3 ( - 1 )n - 2 2 ( - 1 )n - 1 1 1 - 2n 2 -( - 1 )n ( - 1 )n - 1 2 n - 2 ( - 1 )n + 2 2 3 2 2 n - 2 ( - 1 )n + 2 n -( - 1 )n 3 2n + 1 - 1 2 2 n + 1 - 2 ( - 1 )n + 2 - 1 2 1 2 2 n + 1 -( - 1 )n - 1 - 1 2n + 1 1 1 5 2 -1 - 2 n + 1 -( - 1 )n - 1 - 1 2 3 2 practica2mates (1).wxmx 10 / 10 (%i166) T:transpose(matrix([1,0,0,0,0,0,0])); 1 0 0 (%o166) 0 0 0 0 (%i167) J.T; 1 2 2 n -( - 1 )n + (%o167) 1 2 1 2 3 ( - 1 )n - 2 2 n +( - 1 )n - 1 2 ( - 1 )n - 3 2 2 n + 1 + 3 ( - 1 )n - 5 2 ...

Tags:
Comprar Previsualizar