SOLUCIÓN EJERCICIO 1: Básico función matrix
mi_matriz<-matrix(data=c(1,2,3,4,
5,6,7,8,
9,10,11,12),nrow=3, byrow= TRUE)
print(mi_matriz)
## [,1] [,2] [,3] [,4]
## [1,] 1 2 3 4
## [2,] 5 6 7 8
## [3,] 9 10 11 12
mi_matriz2<-matrix(data=c(1,2,3,4,
5,6,7,8,
9,10,11,12),nrow=3, byrow= FALSE) |> print()
## [,1] [,2] [,3] [,4]
## [1,] 1 4 7 10
## [2,] 2 5 8 11
## [3,] 3 6 9 12
practica02
mi_matriz5<-matrix(data=c(1,2,3,4,
5,6,7,8,
9,10,11,12),ncol= 2, byrow= FALSE) |> print()
## [,1] [,2]
## [1,] 1 7
## [2,] 2 8
## [3,] 3 9
## [4,] 4 10
## [5,] 5 11
## [6,] 6 12
print(mi_matriz5)
## [,1] [,2]
## [1,] 1 7
## [2,] 2 8
## [3,] 3 9
## [4,] 4 10
## [5,] 5 11
## [6,] 6 12
Nota: Poner print ayuda a que muestre o ejecute lo que quiero el
código. Al utilizar los comandos Ctrl + Alt+ R se ejecuta todos los
chunks
mi_matriz6<-matrix(data=c(1,2,3,4,
5,6,7,8,
9,10,11,12),ncol= 3, byrow= FALSE) |> print()
## [,1] [,2] [,3]
## [1,] 1 5 9
## [2,] 2 6 10
## [3,] 3 7 11
## [4,] 4 8 12
Operador PAY |> ctrl+ shif+ m para que se active esta función
esta en la configuración tools-global options-code . pay |> hace que
lo que esta a la izquierda lo pasa como argumento a la derecha
EJERCICIO 2 COMBINANDO VECTORES: rbind() y cbind()
ana <- c(10, 20, 30)
beto <- c(15, 25, 35)
unir_filas<-rbind(ana,beto) |> print() #se crea el objeto unir filas y se muestra
## [,1] [,2] [,3]
## ana 10 20 30
## beto 15 25 35
unir_columnas<-cbind(ana,beto) |> print()
## ana beto
## [1,] 10 15
## [2,] 20 25
## [3,] 30 35
# rownames(unir_filas)
rownames(unir_filas)<-c("maria","jose")
colnames(unir_filas)<-c("examen 1", "examen 2", "examen 3")
unir_filas
## examen 1 examen 2 examen 3
## maria 10 20 30
## jose 15 25 35
EJERCICIO 3: OPERACIONES ELEMENTALES
El comando sample nos permite generar numeros aleatorios y también
extraer los mismos mediante la herramienta “size”.Asimimo, podemos
fijarlos para extraer los mismos numeros siempre, al cual nombraremos
“balon semilla”, con el comando set.seed, usado a menudo en examen
Crea un matriz de numeros aleatorios
set.seed(50)
(mi_matriz_aleatoria<-matrix(data= sample( x= 1:100, size= 9),nrow= 3, byrow= TRUE)) |> print()
## [,1] [,2] [,3]
## [1,] 11 52 95
## [2,] 98 46 67
## [3,] 8 16 18
#crear una matriz traspuesta
#Sin guardar
mi_matriz_aleatoria |> t() #no se crea un objeto
## [,1] [,2] [,3]
## [1,] 11 98 8
## [2,] 52 46 16
## [3,] 95 67 18
#Con guardado
transpuesta_mi_matriz_aleatoria<-t(mi_matriz_aleatoria) |> print() #se crea y se muestra el objeto
## [,1] [,2] [,3]
## [1,] 11 98 8
## [2,] 52 46 16
## [3,] 95 67 18
#extrayendo el elemento 2,3
transpuesta_mi_matriz_aleatoria[2,3]
## [1] 16
#Multiplicar la matriz por un escalas( por ejempo 10)
10*transpuesta_mi_matriz_aleatoria |> print()
## [,1] [,2] [,3]
## [1,] 11 98 8
## [2,] 52 46 16
## [3,] 95 67 18
## [,1] [,2] [,3]
## [1,] 110 980 80
## [2,] 520 460 160
## [3,] 950 670 180
EJERCICIO 4 Matriz Identidad y Diagonales
matriz_identidad<-diag(x= 1, nrow=3, ncol=3) |> print()
## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0
## [3,] 0 0 1
#creando una matriz diagonal con los elementos en la diagonal principal
matriz_diagonal<-diag(x=c(5,10,15), nrow=3, ncol=3) |> print()
## [,1] [,2] [,3]
## [1,] 5 0 0
## [2,] 0 10 0
## [3,] 0 0 15
SOLUCIÓN EJERCICIO 5 Inversion de matrices
#Ingreso o matriz
M<-matrix(data =c(1,2,
3,4), nrow=2, byrow= TRUE) |> print()
## [,1] [,2]
## [1,] 1 2
## [2,] 3 4
#Calculo de la inversa
M_inversa<-solve(M) |> print()
## [,1] [,2]
## [1,] -2.0 1.0
## [2,] 1.5 -0.5
#Verificación
M%*%M_inversa|> round(digits=0) |> print()
## [,1] [,2]
## [1,] 1 0
## [2,] 0 1
M%*%M_inversa |> round(digits = 0) |> print()
## [,1] [,2]
## [1,] 1 0
## [2,] 0 1
#matriz no invertible
(matriz_no_invirtible_1<-matrix(data=c(2,4,
0,0),nrow=2, byrow=TRUE)) |> print()
## [,1] [,2]
## [1,] 2 4
## [2,] 0 0
ifelse(det(matriz_no_invirtible_1!=0),
solve(matriz_no_invirtible_1),"matriz singular")
## [1] "matriz singular"
SOLUCIÓN EJERCICIO 6 Rango de una matriz
#Crea una matriz de donde la tercera fila sea la suma de la primera y la segunda (esto la hace linealmente dependiente
#antes de seguir con el ultimo paso de calcular el rango, asegurarse de volver a correr el chunk crt+enter
library(matlib)
fila1<-c(2,3,5,6)
fila2<-c(0,8,1,-7)
fila3<-fila1+fila2
(matriz_para_rango<-matrix(data=c(fila1,
fila2,
fila3),nrow=3, byrow=TRUE)) |> print()
## [,1] [,2] [,3] [,4]
## [1,] 2 3 5 6
## [2,] 0 8 1 -7
## [3,] 2 11 6 -1
rango<-matlib::R(X= matriz_para_rango) |> print()
## [1] 2
library(QR)
SOLUCIÓN EJERCICIO 7 Autovalores y autovectores
#creando la matriz simetrica
s<-matrix(data=c(2,1,
1,2),nrow=2,byrow = TRUE) |> print()
## [,1] [,2]
## [1,] 2 1
## [2,] 1 2
#calcular los autovalores y tambien los autovectores
resultado<-eigen(s)
#autovalores
resultado$values
## [1] 3 1
#verificar los autovalores
#el determinante menos la matriz identidad deberia de dar cero---concepto de autovalores
det(s-resultado$values[1]*diag(x=1,2))==0 #para verificar igualdad,igual,igual
## [1] TRUE
#verificando el segundo autovalor
det(s-resultado$values[2]*diag(x=1,2))
## [1] 0
SOLUCIÓN EJERCICIO 8 Sistemas de ecuaciones lineales
A<-matrix(data=c(2,3,1,
1,-2,4,
3,1,-1), nrow = 3, byrow= TRUE) |> print()
## [,1] [,2] [,3]
## [1,] 2 3 1
## [2,] 1 -2 4
## [3,] 3 1 -1
B<-matrix(data=c(1,-3,4),ncol=1, byrow = TRUE) |> print()
## [,1]
## [1,] 1
## [2,] -3
## [3,] 4
#matriz aumentada s
s<-cbind(A,B) |> print()
## [,1] [,2] [,3] [,4]
## [1,] 2 3 1 1
## [2,] 1 -2 4 -3
## [3,] 3 1 -1 4
#teorema de roche frobenius
matlib::R(s)==matlib::R(A)
## [1] TRUE
#resolver el sistema
solucion<-solve(A,B) |> print()
## [,1]
## [1,] 1
## [2,] 0
## [3,] -1
#verificación
A%*%solucion-B #nos da un vector de ceros
## [,1]
## [1,] 0
## [2,] 0
## [3,] 0
EJERCICIO 9: ELIMINACIÓN GAUSIANA
Nota: No es necesario volver a escribir libreria, si ya la hemos
usado en operaciones anteriores
library(matlib)
matlib::gaussianElimination(A,B,verbose = TRUE) # SI le quito el verbose me da solo la solucion de la matriz escalonada, la ultima solución, si quiero ver toda la socución mejor dejar con verbose.
##
## Initial matrix:
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 2 3 1 1
## [2,] 1 -2 4 -3
## [3,] 3 1 -1 4
##
## row: 1
##
## exchange rows 1 and 3
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 3 1 -1 4
## [2,] 1 -2 4 -3
## [3,] 2 3 1 1
##
## multiply row 1 by 0.3333333
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0.3333333 -0.3333333 1.333333
## [2,] 1 -2.0000000 4.0000000 -3.000000
## [3,] 2 3.0000000 1.0000000 1.000000
##
## subtract row 1 from row 2
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0.3333333 -0.3333333 1.333333
## [2,] 0 -2.3333333 4.3333333 -4.333333
## [3,] 2 3.0000000 1.0000000 1.000000
##
## multiply row 1 by 2 and subtract from row 3
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0.3333333 -0.3333333 1.333333
## [2,] 0 -2.3333333 4.3333333 -4.333333
## [3,] 0 2.3333333 1.6666667 -1.666667
##
## row: 2
##
## multiply row 2 by -0.4285714
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0.3333333 -0.3333333 1.333333
## [2,] 0 1.0000000 -1.8571429 1.857143
## [3,] 0 2.3333333 1.6666667 -1.666667
##
## multiply row 2 by 0.3333333 and subtract from row 1
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0.000000 0.2857143 0.7142857
## [2,] 0 1.000000 -1.8571429 1.8571429
## [3,] 0 2.333333 1.6666667 -1.6666667
##
## multiply row 2 by 2.333333 and subtract from row 3
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0.2857143 0.7142857
## [2,] 0 1 -1.8571429 1.8571429
## [3,] 0 0 6.0000000 -6.0000000
##
## row: 3
##
## multiply row 3 by 0.1666667
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0.2857143 0.7142857
## [2,] 0 1 -1.8571429 1.8571429
## [3,] 0 0 1.0000000 -1.0000000
##
## multiply row 3 by 0.2857143 and subtract from row 1
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0.000000 1.000000
## [2,] 0 1 -1.857143 1.857143
## [3,] 0 0 1.000000 -1.000000
##
## multiply row 3 by 1.857143 and add to row 2
## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches
## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 1
## [2,] 0 1 0 0
## [3,] 0 0 1 -1