Ejercicios R 16-30
Nair González
16/6/2019
## Ejercicio 16
a<-matrix(data=c(3,7,-4,12,-5,9,10,2,6,13,8,11,15,5,4,1),
ncol = 4,nrow = 4,byrow = T) ;a## [,1] [,2] [,3] [,4]
## [1,] 3 7 -4 12
## [2,] -5 9 10 2
## [3,] 6 13 8 11
## [4,] 15 5 4 1v<-c(a[,2]);v## [1] 7 9 13 5w<-c(a[2,]);w## [1] -5 9 10 2
##Ejercicio 17
a<-matrix(data=c(3,7,-4,12,-5,9,10,2,6,13,8,11,15,5,4,1),
ncol = 4,nrow = 4,byrow = T) ;a## [,1] [,2] [,3] [,4]
## [1,] 3 7 -4 12
## [2,] -5 9 10 2
## [3,] 6 13 8 11
## [4,] 15 5 4 1a1<-a[,-1];a1## [,1] [,2] [,3]
## [1,] 7 -4 12
## [2,] 9 10 2
## [3,] 13 8 11
## [4,] 5 4 1b1<-a[-1,];b1## [,1] [,2] [,3] [,4]
## [1,] -5 9 10 2
## [2,] 6 13 8 11
## [3,] 15 5 4 1c1<-a[-c(3,4),-1];c1## [,1] [,2] [,3]
## [1,] 7 -4 12
## [2,] 9 10 2
#Ejercicio 18
a<-c(2,4,7)
length(a)## [1] 3abs(a)## [1] 2 4 7b<-c(2,-4,7)
length(b)## [1] 3abs(b)## [1] 2 4 7
##Ejercicio 19
a<-matrix(data=c(3,7,-4,12,-5,9,10,2,6,13,8,11,15,5,4,1),
ncol = 4,nrow = 4,byrow = T) ;a## [,1] [,2] [,3] [,4]
## [1,] 3 7 -4 12
## [2,] -5 9 10 2
## [3,] 6 13 8 11
## [4,] 15 5 4 1##Maximo y minimo por cada columna
max(a[,1]);min(a[,1])## [1] 15## [1] -5for(i in 1:4) {
mx<-max(a[,i])
print(mx)
}## [1] 15
## [1] 13
## [1] 10
## [1] 12for(i in 1:4) {
mn<-min(a[,i])
print(mn)
}## [1] -5
## [1] 5
## [1] -4
## [1] 1##Maximo y minimo por cada fila
max(a[1,]);min(a[1,])## [1] 12## [1] -4for(i in 1:4) {
mx<-max(a[i,])
print(mx)
}## [1] 12
## [1] 10
## [1] 13
## [1] 15for(i in 1:4) {
mn<-min(a[i,])
print(mn)
}## [1] -4
## [1] -5
## [1] 6
## [1] 1
##Ejercicio 20
a<-matrix(data=c(3,7,-4,12,-5,9,10,2,6,13,8,11,15,5,4,1),
ncol = 4,nrow = 4,byrow = T) ;a## [,1] [,2] [,3] [,4]
## [1,] 3 7 -4 12
## [2,] -5 9 10 2
## [3,] 6 13 8 11
## [4,] 15 5 4 1##Ordenar cada columna
ax1<-matrix(sort(a[,1]))
ax2<-matrix(sort(a[,2]))
ax3<-matrix(sort(a[,3]))
ax4<-matrix(sort(a[,4]))
cbind(ax1,ax2,ax3,ax3)## [,1] [,2] [,3] [,4]
## [1,] -5 5 -4 -4
## [2,] 3 7 4 4
## [3,] 6 9 8 8
## [4,] 15 13 10 10##Ordenar cada fila
ay1<-(sort(a[1,]));ay1## [1] -4 3 7 12ay2<-(sort(a[2,]));ay2## [1] -5 2 9 10ay3<-(sort(a[3,]))
ay4<-(sort(a[4,]))
rbind(ay1,ay2,ay3,ay3)## [,1] [,2] [,3] [,4]
## ay1 -4 3 7 12
## ay2 -5 2 9 10
## ay3 6 8 11 13
## ay3 6 8 11 13
###Ejercicio 21
a<-matrix(data=c(1,4,2,2,4,100,7,9,7,3,pi,42),
ncol = 3,nrow = 4,byrow = T) ;a## [,1] [,2] [,3]
## [1,] 1 4.000000 2
## [2,] 2 4.000000 100
## [3,] 7 9.000000 7
## [4,] 3 3.141593 42b<-log(a);b## [,1] [,2] [,3]
## [1,] 0.0000000 1.386294 0.6931472
## [2,] 0.6931472 1.386294 4.6051702
## [3,] 1.9459101 2.197225 1.9459101
## [4,] 1.0986123 1.144730 3.7376696c<-b[2,];c## [1] 0.6931472 1.3862944 4.6051702sum(c)## [1] 6.684612e<-a[,1]*b[,2]
max(e)## [1] 15.38057a[1,]/b[-4,-c(1,2)]## [1] 1.442695 0.868589 1.027797
##Ejercicio 22
a<-matrix(data=c(3,-2,1,6,8,-5,7,9,10),
ncol = 3,nrow = 3,byrow = T) ;a## [,1] [,2] [,3]
## [1,] 3 -2 1
## [2,] 6 8 -5
## [3,] 7 9 10b<-matrix(data=c(6,9,-4,7,5,3,-8,2,1),
ncol = 3,nrow = 3,byrow = T) ;b## [,1] [,2] [,3]
## [1,] 6 9 -4
## [2,] 7 5 3
## [3,] -8 2 1c<-matrix(data=c(-7,-5,2,10,6,1,3,-9,8),
ncol = 3,nrow = 3,byrow = T) ;c## [,1] [,2] [,3]
## [1,] -7 -5 2
## [2,] 10 6 1
## [3,] 3 -9 8d<-array(c(a,b,c),dim = c(3,3,3));d## , , 1
##
## [,1] [,2] [,3]
## [1,] 3 -2 1
## [2,] 6 8 -5
## [3,] 7 9 10
##
## , , 2
##
## [,1] [,2] [,3]
## [1,] 6 9 -4
## [2,] 7 5 3
## [3,] -8 2 1
##
## , , 3
##
## [,1] [,2] [,3]
## [1,] -7 -5 2
## [2,] 10 6 1
## [3,] 3 -9 8max(d)## [1] 10max(d[,,1])## [1] 10max(d[,,2])## [1] 9max(d[,,3])## [1] 10
##Ejercicio 23
a<-matrix(data=c(-7,16,4,9),
ncol = 2,nrow = 2,byrow = T) ;a## [,1] [,2]
## [1,] -7 16
## [2,] 4 9b<-matrix(data=c(6,-5,12,-2),
ncol = 2,nrow = 2,byrow = T) ;b## [,1] [,2]
## [1,] 6 -5
## [2,] 12 -2c<-matrix(data=c(-3,-9,6,8),
ncol = 2,nrow = 2,byrow = T) ;c## [,1] [,2]
## [1,] -3 -9
## [2,] 6 8a+b+c## [,1] [,2]
## [1,] -4 2
## [2,] 22 15a-b+c## [,1] [,2]
## [1,] -16 12
## [2,] -2 19(a+b)+c## [,1] [,2]
## [1,] -4 2
## [2,] 22 15a+(b+c)## [,1] [,2]
## [1,] -4 2
## [2,] 22 15
##Ejercicio 24
f<-matrix(data=c(1,2,3,4,5,400,550,700,500,600,2,0.5,0.75,1.5,3),
ncol=5,nrow = 3, byrow = T, dimnames = list(c("Path segment",
"Force (N)",
"Distance (m)"),c("C1",
"C2", "C3", "C4", "C5")));f ## C1 C2 C3 C4 C5
## Path segment 1 2.0 3.00 4.0 5
## Force (N) 400 550.0 700.00 500.0 600
## Distance (m) 2 0.5 0.75 1.5 3#Trabajo*segmento
t<-f[2,]*f[3,];t## C1 C2 C3 C4 C5
## 800 275 525 750 1800rbind(f,t)## C1 C2 C3 C4 C5
## Path segment 1 2.0 3.00 4.0 5
## Force (N) 400 550.0 700.00 500.0 600
## Distance (m) 2 0.5 0.75 1.5 3
## t 800 275.0 525.00 750.0 1800#Trabajo total
sum(t)## [1] 4150
#Ejercicio 25
w<-matrix(data=c(1,2,3,4,5,5,5.50,6.50,6,6.25,40,43,37,50,45
,1000,1100,1000,1200,1100),
ncol=5,nrow = 4, byrow = T, dimnames = list(c("Worker",
"Hourly wage ($)",
"Hours worked", "Output (widgets"),c("C1",
"C2", "C3", "C4", "C5")));w ## C1 C2 C3 C4 C5
## Worker 1 2.0 3.0 4 5.00
## Hourly wage ($) 5 5.5 6.5 6 6.25
## Hours worked 40 43.0 37.0 50 45.00
## Output (widgets 1000 1100.0 1000.0 1200 1100.00##Cuanto gano cada trabajador
Ganancia<-w[2,]*w[3,];Ganancia## C1 C2 C3 C4 C5
## 200.00 236.50 240.50 300.00 281.25rbind(w,Ganancia)## C1 C2 C3 C4 C5
## Worker 1 2.0 3.0 4 5.00
## Hourly wage ($) 5 5.5 6.5 6 6.25
## Hours worked 40 43.0 37.0 50 45.00
## Output (widgets 1000 1100.0 1000.0 1200 1100.00
## Ganancia 200 236.5 240.5 300 281.25##Cuanto se pago en total
sum(Ganancia)## [1] 1258.25##Cuantos widgets se hicieron
sum(w[4,])## [1] 5400
##Ejercicio 26
##Asumiendo que los dos buzos empiezan en 0,0,0
##Distancia entre el buzo1y el punto inicial
dis<-sqrt((60^2)+(25)^2+(30)^2);dis## [1] 71.58911##Como debe bucear el buzo 1 para llegar al buzo 2
60-30## [1] 30#Debe nadar 30 ft al oeste
-25+55## [1] 30##Debe nadar 30 ft al sur
30-20## [1] 10#Debe subir 10 ft
## Que tan lejos en linea recta el buzo 1 para llegar al buzo 2
dis2<-sqrt((30^2+30^2+10^2));dis2## [1] 43.58899##Ejercicio 27
s<-matrix(data=c(1,2,3,4,5,11,7,8,10,9
,1000,800,900,1200,700),
ncol=5,nrow = 3, byrow = T, dimnames = list(c("Spring",
"Force (N)",
"Spring Constant k (N/m)"),c("C1",
"C2", "C3", "C4", "C5")));s ## C1 C2 C3 C4 C5
## Spring 1 2 3 4 5
## Force (N) 11 7 8 10 9
## Spring Constant k (N/m) 1000 800 900 1200 700x<-s[2,]/s[3,];x## C1 C2 C3 C4 C5
## 0.011000000 0.008750000 0.008888889 0.008333333 0.012857143rbind(s,x)## C1 C2 C3 C4
## Spring 1.0e+00 2.00e+00 3.000000e+00 4.000000e+00
## Force (N) 1.1e+01 7.00e+00 8.000000e+00 1.000000e+01
## Spring Constant k (N/m) 1.0e+03 8.00e+02 9.000000e+02 1.200000e+03
## x 1.1e-02 8.75e-03 8.888889e-03 8.333333e-03
## C5
## Spring 5.00000000
## Force (N) 9.00000000
## Spring Constant k (N/m) 700.00000000
## x 0.01285714##Potencial
p<-(s[3,]*x^2)/2;p## C1 C2 C3 C4 C5
## 0.06050000 0.03062500 0.03555556 0.04166667 0.05785714
##Ejercicio 28
m<-matrix(data=c(1,2,3,4,5,300,550,400,250,500
,5,3,6,3,2, 4,2,5,5,4,6,4,3,4,3),
ncol=5,nrow = 5, byrow = F, dimnames = list(c("R1",
"R2","R3", "R4", "R5"),c("Material",
"Prince($/ton)", "May", "June", "July")));m ## Material Prince($/ton) May June July
## R1 1 300 5 4 6
## R2 2 550 3 2 4
## R3 3 400 6 5 3
## R4 4 250 3 5 4
## R5 5 500 2 4 3##Precio pagado cada mes
pp<-m[,-c(1,2)]*m[,2];pp## May June July
## R1 1500 1200 1800
## R2 1650 1100 2200
## R3 2400 2000 1200
## R4 750 1250 1000
## R5 1000 2000 1500#Precio pagado en mayo
sum(pp[,1])## [1] 7300##Precio pagado en Junio
sum(pp[,2])## [1] 7550##Precio pagado en Julio
sum(pp[,3])## [1] 7700##Precio de cada material en los tres meses
pm<-pp[,1]+pp[,2]+pp[,3];pm## R1 R2 R3 R4 R5
## 4500 4950 5600 3000 4500##Precio de todos los materiales en los tres meses
sum(pm)## [1] 22550
##Ejercicio 29
a<-matrix(data=c(11,5,-9,-4),
ncol = 2,nrow = 2,byrow = T);a## [,1] [,2]
## [1,] 11 5
## [2,] -9 -4b<-matrix(data=c(-7,-8,6,2),
ncol = 2,nrow = 2,byrow = T);b## [,1] [,2]
## [1,] -7 -8
## [2,] 6 2a%*%b## [,1] [,2]
## [1,] -47 -78
## [2,] 39 64b%*%a## [,1] [,2]
## [1,] -5 -3
## [2,] 48 22##Ejercicio 30
a<-matrix(data=c(3,-2,1,6,8,-5,7,9,10),
ncol = 3,nrow = 3,byrow = T) ;a## [,1] [,2] [,3]
## [1,] 3 -2 1
## [2,] 6 8 -5
## [3,] 7 9 10b<-matrix(data=c(6,9,-4,7,5,3,-8,2,1),
ncol = 3,nrow = 3,byrow = T) ;b## [,1] [,2] [,3]
## [1,] 6 9 -4
## [2,] 7 5 3
## [3,] -8 2 1c<-matrix(data=c(-7,-5,2,10,6,1,3,-9,8),
ncol = 3,nrow = 3,byrow = T) ;c## [,1] [,2] [,3]
## [1,] -7 -5 2
## [2,] 10 6 1
## [3,] 3 -9 8a%*%(b+c)## [,1] [,2] [,3]
## [1,] -42 -17 -5
## [2,] 155 147 -25
## [3,] 96 57 112a%*%b+a%*%c## [,1] [,2] [,3]
## [1,] -42 -17 -5
## [2,] 155 147 -25
## [3,] 96 57 112a%*%(b%*%c)## [,1] [,2] [,3]
## [1,] 167 287 -125
## [2,] -99 -111 308
## [3,] 1132 562 250(a%*%b)%*%c## [,1] [,2] [,3]
## [1,] 167 287 -125
## [2,] -99 -111 308
## [3,] 1132 562 250