Solución ejercicio 1
mi_matriz<-matrix(data = 1:12, 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 = 1:12, nrow = 3, byrow = FALSE ) |> print()
## [,1] [,2] [,3] [,4]
## [1,] 1 4 7 10
## [2,] 2 5 8 11
## [3,] 3 6 9 12
Solución ejercicio 2
ana<- c(10,20,30)
beto<- c(15, 25, 35)
unir_filas<-rbind(ana, beto) |> print()
## [,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
colnames(unir_filas)<-c("examen1", "examen2", "examen3")
unir_filas
## examen1 examen2 examen3
## ana 10 20 30
## beto 15 25 35
Solución ejercicio 3
#Creación de la matriz:
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()
## [,1] [,2] [,3]
## [1,] 11 98 8
## [2,] 52 46 16
## [3,] 95 67 18
#Con guardado:
transupuesta_mi_matriz_aletaoria<-t(mi_matriz_aleatoria) |> print()
## [,1] [,2] [,3]
## [1,] 11 98 8
## [2,] 52 46 16
## [3,] 95 67 18
#Extrayendo el elemnto 2,3
transupuesta_mi_matriz_aletaoria[2,3] |> print()
## [1] 16
#multiplicando la matriz por un escalar
10*transupuesta_mi_matriz_aletaoria |> 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
matriz_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 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 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 autovales y autovectores
resultado<-eigen(s)
#autovalores
resultado$values
## [1] 3 1
#verificar los autovalores
det(s-resultado$values[1]*diag(x = 1,nrow = 2))
## [1] 0
det(s-resultado$values[2]*diag(x = 1,nrow = 2))
## [1] 0
Solución ejercicio 8
library(matlab)
##
## Attaching package: 'matlab'
## The following object is masked from 'package:stats':
##
## reshape
## The following objects are masked from 'package:utils':
##
## find, fix
## The following object is masked from 'package:base':
##
## sum
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
#matrix 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
# solucion
solucion<-solve(A,B) |> print()
## [,1]
## [1,] 1
## [2,] 0
## [3,] -1
#Verificacion
A%*%solucion-B
## [,1]
## [1,] 0
## [2,] 0
## [3,] 0
Solución ejercicio 9
library(matlib)
## Warning in rgl.init(initValue, onlyNULL): RGL: unable to open X11 display
## Warning: 'rgl.init' failed, will use the null device.
## See '?rgl.useNULL' for ways to avoid this warning.
##
## Attaching package: 'matlib'
## The following object is masked from 'package:matlab':
##
## size
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