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 12mi_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 12ana <- 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 35unir_columnas<-cbind(ana,beto) |> print()## ana beto
## [1,] 10 15
## [2,] 20 25
## [3,] 30 35rownames(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#Creación de la matrix:
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#Calculando la transpuesta:
#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] |> print()## [1] 16#multiplicando la matriz por un escalar:
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#Solución ejercicio 4:
#creando una matriz identidad:
matrix_identidad<-diag(x = 1,nrow = 3) |> print()## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0
## [3,] 0 0 1#creando una matriz diagonal con los elementos c(5, 10, 15) en la diagonal principal.
matriz_diagonal<-diag(x = c(5, 10, 15),nrow = 3) |> print()## [,1] [,2] [,3]
## [1,] 5 0 0
## [2,] 0 10 0
## [3,] 0 0 15#Solución ejercicio 5
#ingreso de la matriz
M<-matrix(data = c(1,2,
3,4),nrow = 2,byrow = TRUE) |> print()## [,1] [,2]
## [1,] 1 2
## [2,] 3 4#1- Cálculando la inversa
M_inversa<-solve(M) |> print()## [,1] [,2]
## [1,] -2.0 1.0
## [2,] 1.5 -0.5#2-verificación
M %*% M_inversa |> round(digits = 0) |> print()## [,1] [,2]
## [1,] 1 0
## [2,] 0 1M_inversa %*% M |> round(digits = 0) |> print()## [,1] [,2]
## [1,] 1 0
## [2,] 0 1#3
matriz_no_invertible_1<-matrix(data = c(2,4,
0,0),nrow = 2,byrow = TRUE) |> print()## [,1] [,2]
## [1,] 2 4
## [2,] 0 0ifelse(det(matriz_no_invertible_1!=0),
solve(matriz_no_invertible_1),"Matriz Singular")## [1] "Matriz Singular"#Solución Ejercicio 6
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 -1rango<-matlib::R(X = matriz_para_rango) |> print()## [1] 2#Solución ejercicio 7
#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 también los autovectores)
resultado<-eigen(S)
#autovalores
resultado$values## [1] 3 1#verificar los autovalores
#verificando el primer autovalor
det(S-resultado$values[1]*diag(x = 1,2))## [1] 0#verificando el segundo autovalor
det(S-resultado$values[2]*diag(x = 1,2))## [1] 0#Solución de ejercicio 8
library(matlib)
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 -1B<-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 Rouche 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## [,1]
## [1,] 0
## [2,] 0
## [3,] 0#ejercicio 9:
library(matlib)
matlib::gaussianElimination(A,B,verbose = TRUE,fractions = TRUE)##
## 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 1/3## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches## [,1] [,2] [,3] [,4]
## [1,] 1 1/3 -1/3 4/3
## [2,] 1 -2 4 -3
## [3,] 2 3 1 1
##
## 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 1/3 -1/3 4/3
## [2,] 0 -7/3 13/3 -13/3
## [3,] 2 3 1 1
##
## 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 1/3 -1/3 4/3
## [2,] 0 -7/3 13/3 -13/3
## [3,] 0 7/3 5/3 -5/3
##
## row: 2
##
## multiply row 2 by -3/7## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches## [,1] [,2] [,3] [,4]
## [1,] 1 1/3 -1/3 4/3
## [2,] 0 1 -13/7 13/7
## [3,] 0 7/3 5/3 -5/3
##
## multiply row 2 by 1/3 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 2/7 5/7
## [2,] 0 1 -13/7 13/7
## [3,] 0 7/3 5/3 -5/3
##
## multiply row 2 by 7/3 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 2/7 5/7
## [2,] 0 1 -13/7 13/7
## [3,] 0 0 6 -6
##
## row: 3
##
## multiply row 3 by 1/6## Warning in printMatrix(A): Function is deprecated. See latexMatrix() and Eqn()
## for more recent approaches## [,1] [,2] [,3] [,4]
## [1,] 1 0 2/7 5/7
## [2,] 0 1 -13/7 13/7
## [3,] 0 0 1 -1
##
## multiply row 3 by 2/7 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 1
## [2,] 0 1 -13/7 13/7
## [3,] 0 0 1 -1
##
## multiply row 3 by 13/7 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