Nivel 3: 6. Determine el Rango de cada matriz. a)

B=61

71

61F12(-1)61F2110F12(-6)10

71106101

Rango (B) = 2 Con Matlab:>> B=[6 1;7 1]B = 6 1 7 1>> rank(B)ans = 2b)2082081-40

A=-140F2(-1)1-40F12208

210210210

1-401-401-40

F23(-1)208F12(-2)088F2301-8

01-801-8088

1-401-401-40

F3(1/8)01-8F23(-1)01-8F3(1/9)01-8

011009001

Rango (A) = 3

Con Matlab:>> A=[2 0 8;-1 4 0;2 1 0]A = 2 0 8 -1 4 0 2 1 0>> rank(A)ans = 3

c)12-112-112-1

C=014F13(-1)014F3(1/3)014

1-120-330-11

12-112-1

F23(1)014F3(1/5)014

005001

Rango (C) = 3 Con Matlab:>> C=[1 2 -1;0 1 4;1 -1 2]C = 1 2 -1 0 1 4 1 -1 2>> rank(C)ans = 3

7. Calcule los cofactores de la matriz 6 (C).

12-1

C=014

1-12

COFACTOR: Aij = (-1)i+j . det Mij

A11=(-1)1+1det14A11= 1*[(2)(1)-(-1)(4)= 6

-12

A12=(-1)1+2det04A12= -1*[(0)(2)-(1)(4)= 4

12

A13=(-1)1+3det01A13= 1*[(0)(-1)-(1)(1)= -1

1-1

A21=(-1)2+1det2-1A21= -1*[(2)(2)-(-1)(-1)= -3

-12

A22=(-1)2+2det1-1A22= 1*[(1)(2)-(1)(-1)= 3

12

A23=(-1)2+3det12A23= -1*[(1)(-1)-(1)(2)= 3

1-1

A31=(-1)3+1det2-1A31= 1*[(2)(4)-(1)(-1)= 9

14

A32=(-1)3+2det1-1A32= -1*[(1)(4)-(0)(-1)= -4

04

A33=(-1)3+3det12A33= 1*[(1)(1)-(0)(2)= 1

01

FACULTAD DE INGENIERIAESPECIALIDAD DE INGENIERIA CIVIL

PRCTICA 02RANGO Y DETERMINANTES

Curso: MTODOS NUMRICOS

Lima, abril del 2015