Solución Práctica de Matrices
Vanessa MM24056
2026-02-10
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Solución Ejercicio 1
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),ncol = 3,byrow = FALSE) |>
print()## [,1] [,2] [,3]
## [1,] 1 5 9
## [2,] 2 6 10
## [3,] 3 7 11
## [4,] 4 8 12Solución Ejercicio 2
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 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 35solición ejercicio 3
set.seed(50)
(mi_matrix_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 transpuesta:
# sin guardar
mi_matrix_aleatoria |> t() #no se crea un objeto## [,1] [,2] [,3]
## [1,] 11 98 8
## [2,] 52 46 16
## [3,] 95 67 18#Con guadado:
transpuesta_mi_matriz_aleatoria<-t(mi_matrix_aleatoria) |>print() #se crea un 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#multipliplicando la matriz por una escalae
10*transpuesta_mi_matriz_aleatoria[2,3] |>print()## [1] 16## [1] 160#Solucion ejercicio 4
#Creando una matriz identidad:
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_diagona<-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 15solución 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 calculando la inversa
M_inversa<-solve(M) |>print()## [,1] [,2]
## [1,] -2.0 1.0
## [2,] 1.5 -0.5#2 verificacion
M%*% M_inversa |> 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) |> print()## [1] 2 3 5 6fila2<-c(0,8,1,-7)|>print()## [1] 0 8 1 -7(fila3<-fila1+fila2) |>print()## [1] 2 11 6 -1(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 ejerccicio 7
#creando 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$values## [1] 3 1#verificar los autovalores
det(S-resultado$values[1]*diag(x=1,2))==0## [1] TRUE#verificando el segundo valor
det(S-resultado$values[2]*diag(x=1,2))==0## [1] TRUE#Solucion 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<-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#ES DE SOLUCION UNICA
#Resolver sistema
solucion<-solve(A,B) |>print()## [,1]
## [1,] 1
## [2,] 0
## [3,] -1#Verificacion
A%*%solucion-B## [,1]
## [1,] 0
## [2,] 0
## [3,] 0#solucion ejercicio 9
library(matlib)
#para ver con todos los procesos
matlib::gaussianElimination(A,B,verbose = 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 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 -1library(matlib)
#Solo resultado final
matlib::gaussianElimination(A,B)## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 1
## [2,] 0 1 0 0
## [3,] 0 0 1 -1