Taller CE-100PR
Juan Sebastian Herrera Reales
13/1/2022
Ejercicio 1
#1
3*4+6## [1] 18#2
cos(5)## [1] 0.2836622cos(5)*pi/180## [1] 0.004950839#3
x<-4
3*sqrt(6+x)## [1] 9.486833#4
y<- 5.2
#5
x<-3; y<-4
z= (2*x) - (7*y)
z## [1] -22#6
#7
a1 <- c(1, 0, 2, -3)
a2 <- c(0, 5, 2, 2)
a3 <- c(1, 2, 3, 4)
a4 <- c(-2, 0, 1, 3)
A <- rbind(a1, a2, a3, a4)
A## [,1] [,2] [,3] [,4]
## a1 1 0 2 -3
## a2 0 5 2 2
## a3 1 2 3 4
## a4 -2 0 1 3#8
b1 <- c(1,2,3,4)
B <- cbind(b1)
B## b1
## [1,] 1
## [2,] 2
## [3,] 3
## [4,] 4#9
C <- A%*%B
C## b1
## a1 -5
## a2 24
## a3 30
## a4 13#11
#13
x1 <- c(1, 0, 6)
x2 <- c(1, 2, 3)
x3 <- c(4, 5, -2)
X <- rbind(x1, x2, x3)
X## [,1] [,2] [,3]
## x1 1 0 6
## x2 1 2 3
## x3 4 5 -2X2 = cbind(x1, x2, x3)
X2## x1 x2 x3
## [1,] 1 1 4
## [2,] 0 2 5
## [3,] 6 3 -2select(c(X2[,2:3]:X2[0:2,]))## Warning in X2[, 2:3]:X2[0:2, ]: numerical expression has 6 elements: only the
## first used
## Warning in X2[, 2:3]:X2[0:2, ]: numerical expression has 6 elements: only the
## first used## [1] 1sub_ma= X[,1:2]: X[2:3,]## Warning in X[, 1:2]:X[2:3, ]: numerical expression has 6 elements: only the
## first used## Warning in X[, 1:2]:X[2:3, ]: numerical expression has 6 elements: only the
## first used#15
X[0:1,]## [1] 1 0 6#17
x = c(1:9)
x## [1] 1 2 3 4 5 6 7 8 9#19
sm1 <- c(16, 3, 2, 13)
sm2 <- c(5, 10, 11, 8)
sm3 <- c(9, 6, 7, 12)
sm4 <- c(4, 15, 14, 1)
Constante = 34
sm <- rbind(sm1, sm2, sm3, sm4)
sm## [,1] [,2] [,3] [,4]
## sm1 16 3 2 13
## sm2 5 10 11 8
## sm3 9 6 7 12
## sm4 4 15 14 1sum(sm[,1:1])## [1] 34sum(sm[,2:2])## [1] 34sum(sm[,3:3])## [1] 34sum(sm[,4:4])## [1] 34sum(sm[1:1,])## [1] 34sum(sm[2:2,])## [1] 34sum(sm[3:3,])## [1] 34sum(sm[4:4,])## [1] 34sum(diag(sm))## [1] 34Ejercicio 2
#1
w = 2*3+7
w## [1] 13#3
y= 10
Y= 100
#Aunque son la misma letra, estas tienen distinciones en la mayuscula y minuscula, fuera de ello tienen asignados numericos distintos, son variables numericas pero con distintos identificadores y valores.
#5
x = 5.5
y = -2.6
z = 2*x - 3*y
z## [1] 18.8w = 3*y - z + x/y
w## [1] -28.71538#7
r = 6.3
s = 5.8
this_is_the_result = r**2 - s**2
this_is_the_result## [1] 6.05#9
#This line will not be executed
#11
y1 = 7
y2 = 9
y3 = y1 - y2/3
y3## [1] 4y3_2 = y1 - y2 # hay una nota donde dice que el 3 de la ecuacion y3 es un subindice y que no se debe dividir en 3 por lo que se realizo dos veces la formula por que es algo ambigua la explicacion
#13
cost = 175
profit = 25
sale_price = cost + profit
sale_price## [1] 200#15
format.short = round(14/9, 4)
format.short## [1] 1.5556format.large = round(14/9, 16)
format.large ## [1] 1.555556#17
#19
Altura = 5
Base = 7
Area = (Altura*Base)
Area## [1] 35Perimetro = 2*(Altura+Base)
Perimetro## [1] 24#21
x=4/5
z=14/17
#23
radio=2/3
Area=pi*(radio^2)
#25
doble = as.double(Area)
doble## [1] 1.396263is.double(doble)## [1] TRUE#27
y= 9
date = 12Ejercicio 3
#1
sqrt(10)## [1] 3.162278#3
cos(45)## [1] 0.525322#5
cos (45*(pi/180))## [1] 0.7071068#7
atan(1.5)## [1] 0.9827937#9
exp(3)## [1] 20.08554#11
log10(3.5)## [1] 0.544068#12
x= 2.43
round(x, 1)## [1] 2.4#13
#remainder
5 %% 4## [1] 14 %% 5## [1] 4#quotient
4 %/% 5## [1] 05 %/% 4## [1] 1#14
n = -3.6
funcion = sqrt(n**2)
funcion## [1] 3.6abs(n)## [1] 3.6#15
1.5-2*sqrt((6.7/5))## [1] -0.8151674#16
sin(pi)**2 + cos(pi)**2## [1] 1#17
log10(0)## [1] -Inf#No genera error pero el valor dado es -infinito, ya que en ese valor esta indefinido
#19
Raiz_45=round(sqrt(45), 1)
#21
Seno_45= sin(45)
#23
Tangente_45 = tan(45)
#25
Exponente_pi_medios = exp(pi/2)
Exponente_pi_medios## [1] 4.810477Ejercicio 4
#1
w = c(2, 4, -6, 0)
#3
z = (pi/2)*w
z## [1] 3.141593 6.283185 -9.424778 0.000000#5
z[1]## [1] 3.141593#7
sum(z)## [1] 0sum(z[1:4])## [1] 0#9
r = c(1:10)
aumento = r + 2.5
#11
v1 = c(9, 3, -2, 5, 0)
v2 = c(1,2,-4)
vn = c(v1,v2)
vn## [1] 9 3 -2 5 0 1 2 -4#13
v1 = c(0.2, 1.3, -3.5)
v2 = c(0.5, -2.5, 1.0)
suma = v1 + v2
suma## [1] 0.7 -1.2 -2.5anadidos= c(v1 + v2)
anadidos## [1] 0.7 -1.2 -2.5#15
v1 = c(0.2, 1.3, -3.5)
v2 = c(0.5, -2.5, 1.0)
multiplicacion = v1*v2
multiplicacion # no arroja ningun error## [1] 0.10 -3.25 -3.50#17
v1 = c(0.2, 1.3, -3.5)
v2 = c(0.5, -2.5, 1.0)
division = v1/v2
division## [1] 0.40 -0.52 -3.50#19
v1 = c(1,3,5)
v2 = c(3,6)
suma = v1 + v2## Warning in v1 + v2: longitud de objeto mayor no es múltiplo de la longitud de
## uno menorsuma #no da ningun error ya que toma la longitud mas grande entre los vectores, al mas pequeño le da valores nulos o 0 pensaria yo y queda el mismo valor del vector mas grande en esos espacios ## [1] 4 9 8anadidos= c(v1 + v2)## Warning in v1 + v2: longitud de objeto mayor no es múltiplo de la longitud de
## uno menoranadidos## [1] 4 9 8#21
w = c(0.1, 1.3,-2.4)
escalar = w + 5
escalar## [1] 5.1 6.3 2.6#23
w = c(0.1, 1.3,-2.4)
mulp_escalar = 1.5*w
mulp_escalar## [1] 0.15 1.95 -3.60#25
w = c(0.1, 1.3,-2.4)
opera_escalar = 3-2*w/5
opera_escalar## [1] 2.96 2.48 3.96#27
b = c(0, pi/3, 2*pi/3, pi)
exp(b)## [1] 1.000000 2.849654 8.120527 23.140693#29
3**b #sin mensajes de error## [1] 1.000000 3.159659 9.983445 31.544281#31
a = c(1,1,1,1)
#33
vd = c(0.35, -1.0, 0.24, 1.30, -0.30)
sort(vd)## [1] -1.00 -0.30 0.24 0.35 1.30#35
vr = c(2,4,-3,0,1,5,7)
media = mean(vr)
media## [1] 2.285714rango = range(vr)
rango## [1] -3 7mediana = median(vr)
mediana## [1] 2#37
x = c("r", "s", "t", "u", "v")
n = c(1,0,-2,3,5)
y<-paste(x,'+',n)
y## [1] "r + 1" "s + 0" "t + -2" "u + 3" "v + 5"#39
#41Ejercicio 5
#1
a<-c(3,1,0,3,-2,5)
A<-matrix(a,2)
A## [,1] [,2] [,3]
## [1,] 3 0 -2
## [2,] 1 3 5dim(A)## [1] 2 3#3
B<-((3/2)*pi)*A
B## [,1] [,2] [,3]
## [1,] 14.137167 0.00000 -9.424778
## [2,] 4.712389 14.13717 23.561945#5
sub_ma= c(B[1,1], B[2,2])
matriz= matrix(sub_ma)
#7
length(matriz)## [1] 2#9
sumaT= sum(B[,0:1]) + sum(B[,2:2]) + sum(B[,3:3])
sumaT## [1] 47.12389max(B)## [1] 23.56194min(B)## [1] -9.424778#11
a<-c(1,7,3,2,5,1,0,-3,1)
b<-c(1,3,2,3,5,3,-2,7,0)
R<-matrix(a,3)
S<-matrix(b,3)
R## [,1] [,2] [,3]
## [1,] 1 2 0
## [2,] 7 5 -3
## [3,] 3 1 1S## [,1] [,2] [,3]
## [1,] 1 3 -2
## [2,] 3 5 7
## [3,] 2 3 0A<-R+S
B<-R-S
A## [,1] [,2] [,3]
## [1,] 2 5 -2
## [2,] 10 10 4
## [3,] 5 4 1B## [,1] [,2] [,3]
## [1,] 0 -1 2
## [2,] 4 0 -10
## [3,] 1 -2 1#13
De<-R/S
De## [,1] [,2] [,3]
## [1,] 1.000000 0.6666667 0.0000000
## [2,] 2.333333 1.0000000 -0.4285714
## [3,] 1.500000 0.3333333 Inf#15
x<-c(1,2,-3,5,-2,3,5,-2,0,6,2,4,1,2,1,4)
X<-matrix(x,4)
X## [,1] [,2] [,3] [,4]
## [1,] 1 -2 0 1
## [2,] 2 3 6 2
## [3,] -3 5 2 1
## [4,] 5 -2 4 4M<-X+5
M## [,1] [,2] [,3] [,4]
## [1,] 6 3 5 6
## [2,] 7 8 11 7
## [3,] 2 10 7 6
## [4,] 10 3 9 9#17
y = X*-3
y## [,1] [,2] [,3] [,4]
## [1,] -3 6 0 -3
## [2,] -6 -9 -18 -6
## [3,] 9 -15 -6 -3
## [4,] -15 6 -12 -12#19
-3*X/2.4+5.5## [,1] [,2] [,3] [,4]
## [1,] 4.25 8.00 5.5 4.25
## [2,] 3.00 1.75 -2.0 3.00
## [3,] 9.25 -0.75 3.0 4.25
## [4,] -0.75 8.00 0.5 0.50#21
B = c(pi/3, (2*pi)/3, (2*pi)/3, pi)
Bb=matrix(B,2)
Bb## [,1] [,2]
## [1,] 1.047198 2.094395
## [2,] 2.094395 3.141593sqrt(Bb)## [,1] [,2]
## [1,] 1.023327 1.447203
## [2,] 1.447203 1.772454#23
exp(1)^B## [1] 2.849654 8.120527 8.120527 23.140693#25
log(B)## [1] 0.0461176 0.7392648 0.7392648 1.1447299#27
exp(4)^B## [1] 65.94297 4348.47466 4348.47466 286751.31314#29
B^(4)## [1] 1.202581 19.241302 19.241302 97.409091#31
cero = c(0, 0, 0, 0, 0, 0)
M_cero=matrix(cero,2)
M_cero## [,1] [,2] [,3]
## [1,] 0 0 0
## [2,] 0 0 0#33
matrix(1,nrow = 4,ncol = 4)## [,1] [,2] [,3] [,4]
## [1,] 1 1 1 1
## [2,] 1 1 1 1
## [3,] 1 1 1 1
## [4,] 1 1 1 1#35
cero = c(1, 0 , 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)
M_cero=matrix(cero,4)
M_cero## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1#36
a<-c(1,2,1,2,2,5,3,3,-3,2,7,-1,0,-3,-2,3)
C<-matrix(a,4)
C## [,1] [,2] [,3] [,4]
## [1,] 1 2 -3 0
## [2,] 2 5 2 -3
## [3,] 1 3 7 -2
## [4,] 2 3 -1 3t(C)## [,1] [,2] [,3] [,4]
## [1,] 1 2 1 2
## [2,] 2 5 3 3
## [3,] -3 2 7 -1
## [4,] 0 -3 -2 3#37
sum_c= C+C
sum_c## [,1] [,2] [,3] [,4]
## [1,] 2 4 -6 0
## [2,] 4 10 4 -6
## [3,] 2 6 14 -4
## [4,] 4 6 -2 6#39
sup= c(C[,1], C[1,2],C[2,2],C[3,2], C[1,3],C[2,3],C[1,4])
infe= c(C[,4], C[4,3],C[3,3],C[2,3], C[3,2],C[3,2],C[4,1])
#41
C_1<-solve(C)
#43
#45
#47
a<-c(1,2,1,2,2,5,3,3,-3,2,7,-1,0,-3,-2, 3, 3,-2, 5, 8, -8, 5, 8, 7, 8)
C<-matrix(a,5)
C## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 5 7 3 -8
## [2,] 2 3 -1 3 5
## [3,] 1 3 0 -2 8
## [4,] 2 -3 -3 5 7
## [5,] 2 2 -2 8 8Ejercicio 6
#1
#Example 8
Cost = 200
sale_price = 250
profit = Cost - sale_price
#3
RectanguloArea = c(a=3,b=6)
#Area de un rectangulo
RectanguloArea[1]*RectanguloArea[2]## a
## 18RectanguloArea = c(a=2.5, b=5.5)
#Area de un rectangulo
RectanguloArea[1]*RectanguloArea[2]## a
## 13.75#5
almacen1 = c()
almacen2 = c()
for(n in 1:4){
almacen1[n] = print(n**2)
}## [1] 1
## [1] 4
## [1] 9
## [1] 16for(m in 1:4){
almacen2[m] = print(n**2)
}## [1] 16
## [1] 16
## [1] 16
## [1] 16almacen_f= almacen2 - almacen1
almacen_f## [1] 15 12 7 0#7
price <- numeric()
for (items in c(3,9)){
if (items<5){
price[items]<-print(items*130)
}
if (items>5){
price[items]<-print(items*160)
}
}## [1] 390
## [1] 1440price## [1] NA NA 390 NA NA NA NA NA 1440Ejercicio 7
#1
x = c(1:7)
y = c(10,15, 23, 43, 30, 10, 12)
plot(x, y)
#3
x = -6:6
y = 2*(x**3) + 5
plot(x, y, xlab = "Eje X", ylab = "Eje Y", main = "Grafico")
#5
y = 2*sin(x/3)
z = 2*cos(x/3)
x= seq(0, 3*pi, pi/4)
plot(x, y, type = "o", col = "blue", pch = "o", ylab = "y", lty = 1, xlab ="Eje X" , main = "grafico Y vs Z")
points(x, z, col = "dark red", pch = "+")
lines(x, z, col = "dark red", lty = 3)
legend (8,2, legend = c ("y", "z"), col = c("blue", "red"),pch = c ("o", "*", "+"),lty=c(1,2),ncol = 1)
#7##Exercise 1
#2
cos(5)## [1] 0.2836622#4
y<-5.2
y## [1] 5.2#6###############################################8
b<-c(1,2,3,4)
b<-t(t(b))
b## [,1]
## [1,] 1
## [2,] 2
## [3,] 3
## [4,] 4#10
a<-c(5,1)
b<-c(2,3)
d<-c(3,-1)
e<-matrix(c(a,b,d),2)
e## [,1] [,2] [,3]
## [1,] 5 2 3
## [2,] 1 3 -1print('..............')## [1] ".............."e<-t(matrix(c(e[1,]/5,e[2,]),3))
e## [,1] [,2] [,3]
## [1,] 1 0.4 0.6
## [2,] 1 3.0 -1.0print('..............')## [1] ".............."e<-t(matrix(c(e[1,],e[2,]-e[1,]),3))
e## [,1] [,2] [,3]
## [1,] 1 0.4 0.6
## [2,] 0 2.6 -1.6print('..............')## [1] ".............."e<-t(matrix(c(e[1,],e[2,]/2.6),3))
e## [,1] [,2] [,3]
## [1,] 1 0.4 0.6000000
## [2,] 0 1.0 -0.6153846print('..............')## [1] ".............."d<-c(0,"x2 =",e[2,3])
m<-c('x1',"0.4 x2",0.6)
f<-t(matrix(c(m,d),3))
f## [,1] [,2] [,3]
## [1,] "x1" "0.4 x2" "0.6"
## [2,] "0" "x2 =" "-0.615384615384615"print('..............')## [1] ".............."d<-c("x1 =",0.6-(e[1,2]*e[2,3]))
d## [1] "x1 =" "0.846153846153846"f[2,2:3]## [1] "x2 =" "-0.615384615384615"#12
b<-c(1,1,4)
a<-c(0,2,5)
d<-c(6,3,-2)
f<-matrix(c(b,a,d),3)
f## [,1] [,2] [,3]
## [1,] 1 0 6
## [2,] 1 2 3
## [3,] 4 5 -2#14
f[1:3,2]## [1] 0 2 5#16
f[1,3]## [1] 6#17
x<-sequence(9)
x## [1] 1 2 3 4 5 6 7 8 9#18
plot(x,((x^3)-2),type = 'l')
##Exercise 2
#2
a<-4
b<--10
c<-3.2#4
x=5.5
y=-2.6
z=2*x-3*y
z## [1] 18.8#6
r=6.3
s=5.8
d=(r+s)-(r*s)
d## [1] -24.44#8
width<-1.5
Width<-2.0
WIDTH<-4.5
width## [1] 1.5Width## [1] 2WIDTH## [1] 4.5#Las variables son diferentes#10
s<-3.5 #Se le asigna un valor a la variable s #12
#y=(2*m)-5
#El error es debido a que la variable m no esta definida #14
centigrade=28
fahrenheit=(centigrade*9/5)+32
fahrenheit## [1] 82.4#16#18#20
radio<-6.45
perimetro<-2*pi*radio
perimetro## [1] 40.52655area<-pi*(radio^2)
area## [1] 130.6981#21
x<-4/5
z<-14/17#22
b<-2*x-z
b ## [1] 0.7764706#24
radio<-2/3
vol<-(4/3)*pi*(radio^3)#26##Exercise 3
#2
factorial(7)## [1] 5040#3
cos(45)## [1] 0.525322#4
rad<-45
deg<-rad*pi/180
cos(deg)## [1] 0.7071068#6
rad<-45
deg<-rad*pi/180
tan(deg)## [1] 1#8
a<-(3/2)*pi
a## [1] 4.712389tan(a)## [1] 5.443746e+15#No se presenta ningun error ya que R esta redondeando el valor de pi, por lo que se toma
#un valor muy cercano a la asintota formada en tan(x) para x=(3/2)*pi, y no se llega a infinitoexp(1)## [1] 2.718282#10
log(3.5,base = exp(1))## [1] 1.252763#12
round(2.43,1)## [1] 2.4#14
abs(-3.6)## [1] 3.6#16
((sin(pi))^2)+((cos(pi))^2)## [1] 1#18
x=(3/2)*pi
y=2*pi
2*sin(x)*cos(y)## [1] -2#20
sqrt(45)## [1] 6.708204#22#24##Exercise 4
#1
w<-c(2,4,-6,0)#2
w[2]## [1] 4#3
z=(pi/2)*w
z## [1] 3.141593 6.283185 -9.424778 0.000000#4
z[4]## [1] 0#6
length(z)## [1] 4#8
min(z) #minimo## [1] -9.424778max(z) #maximo## [1] 6.283185#10
m<-NULL
for (i in sequence(10)){
m[i]<-i*10
}
m## [1] 10 20 30 40 50 60 70 80 90 100#12
a<-c(9,3,-2,5,0)
d<-c(a,4)
d## [1] 9 3 -2 5 0 4#13
a<-c(0.2,1.3,-3.5)
b<-c(0.5,-2.5,1.0)
d<-c(a,b)
d## [1] 0.2 1.3 -3.5 0.5 -2.5 1.0#14
a<-d[1:3]
b<-d[4:6]
a## [1] 0.2 1.3 -3.5b## [1] 0.5 -2.5 1.0#16
a*b## [1] 0.10 -3.25 -3.50#18
d<-0
k<-a*b
for (i in k){
d<-d+i
}
d## [1] -6.65#20
#a<-c(1,3,5)
#b<-c(3,6)
#k<-a-b
# El error se presenta porque a y b no tienen la misma longitud,
#a tiene 3 elementos y b tiene unicamente 2#21
w<-c(0.1,1.3,-2.4)
x<-5+w
x## [1] 5.1 6.3 2.6#22
y<--2-w
y## [1] -2.1 -3.3 0.4#24
z<-w/10
z## [1] 0.01 0.13 -0.24#26
b<-c(0,pi/3,(2/3)*pi,pi)
b## [1] 0.000000 1.047198 2.094395 3.141593sin(b)## [1] 0.000000e+00 8.660254e-01 8.660254e-01 1.224606e-16cos(b)## [1] 1.0 0.5 -0.5 -1.0tan(b)## [1] 0.000000e+00 1.732051e+00 -1.732051e+00 -1.224647e-16#28
m<-sqrt(b)
m## [1] 0.000000 1.023327 1.447203 1.772454#30
b<-c(0,pi/3,(2/3)*pi,pi)
f<-NULL
for (i in b){
f[i+1]<-(3^i)
}
f## [1] 1.000000 3.159659 9.983445 31.544281#32
a<-c(0,0,0,0,0,0)#34
z<-sample.int(x,5)
z## [1] 4 5 2 1 3#36
x<-c("r","s","t","u","v")
x## [1] "r" "s" "t" "u" "v"#37
m<-c(1,0,-2,3,5)
y<-paste(x,'+',m)
v<-unlist(strsplit(y[3],'+'))
v<-paste(v[1],v[5],v[6])
y<-c(y[1:2],v,y[4:5])
y## [1] "r + 1" "s + 0" "t - 2" "u + 3" "v + 5"#38
y[3]## [1] "t - 2"#40
m<-NULL
n<-NULL
for (i in sequence(4)){
m[i]<-paste(x[i],'*(',y[i],')+')
n[i]<-paste('(',y[i],')*',x[i],'+')
}
m<-c(m,paste(x[5],'*(',y[5],')'))
n<-c(n,paste('(',y[5],')*',x[5]))
m<-paste(m[1],m[2],m[3],m[4],m[5])
n<-paste(n[1],n[2],n[3],n[4],n[5])
m## [1] "r *( r + 1 )+ s *( s + 0 )+ t *( t - 2 )+ u *( u + 3 )+ v *( v + 5 )"n## [1] "( r + 1 )* r + ( s + 0 )* s + ( t - 2 )* t + ( u + 3 )* u + ( v + 5 )* v"#El resultado es el mismo porque el producto punto es conmutativo##Exercise 5
#1
a<-c(3,1,0,3,-2,5)
A<-matrix(a,2)
A## [,1] [,2] [,3]
## [1,] 3 0 -2
## [2,] 1 3 5dim(A)## [1] 2 3#2
A[2,2]## [1] 3#3
B<-((3/2)*pi)*A
B## [,1] [,2] [,3]
## [1,] 14.137167 0.00000 -9.424778
## [2,] 4.712389 14.13717 23.561945#4
B[1,3]## [1] -9.424778#6
dim(B)## [1] 2 3#8
n<-dim(B)
elem<-n[1]*n[2]
elem## [1] 6#10
a<-c(1,3,0,-4)
b<-c(5,3,1,0)
d<-c(2,2,-1,1)
matrix(c(a,b,d),3)## [,1] [,2] [,3] [,4]
## [1,] 1 -4 1 2
## [2,] 3 5 0 -1
## [3,] 0 3 2 1#11
a<-c(1,7,3,2,5,1,0,-3,1)
b<-c(1,3,2,3,5,3,-2,7,0)
R<-matrix(a,3)
S<-matrix(b,3)
R## [,1] [,2] [,3]
## [1,] 1 2 0
## [2,] 7 5 -3
## [3,] 3 1 1S## [,1] [,2] [,3]
## [1,] 1 3 -2
## [2,] 3 5 7
## [3,] 2 3 0A<-R+S
B<-R-S
A## [,1] [,2] [,3]
## [1,] 2 5 -2
## [2,] 10 10 4
## [3,] 5 4 1B## [,1] [,2] [,3]
## [1,] 0 -1 2
## [2,] 4 0 -10
## [3,] 1 -2 1#12
Me<-S*R
Me## [,1] [,2] [,3]
## [1,] 1 6 0
## [2,] 21 25 -21
## [3,] 6 3 0#13
De<-R/S
De## [,1] [,2] [,3]
## [1,] 1.000000 0.6666667 0.0000000
## [2,] 2.333333 1.0000000 -0.4285714
## [3,] 1.500000 0.3333333 Inf#14
Mm<-R%*%S
Mm## [,1] [,2] [,3]
## [1,] 7 13 12
## [2,] 16 37 21
## [3,] 8 17 1#15
x<-c(1,2,-3,5,-2,3,5,-2,0,6,2,4,1,2,1,4)
X<-matrix(x,4)
X## [,1] [,2] [,3] [,4]
## [1,] 1 -2 0 1
## [2,] 2 3 6 2
## [3,] -3 5 2 1
## [4,] 5 -2 4 4M<-X+5
M## [,1] [,2] [,3] [,4]
## [1,] 6 3 5 6
## [2,] 7 8 11 7
## [3,] 2 10 7 6
## [4,] 10 3 9 9#16
N<-X-3
N## [,1] [,2] [,3] [,4]
## [1,] -2 -5 -3 -2
## [2,] -1 0 3 -1
## [3,] -6 2 -1 -2
## [4,] 2 -5 1 1#18
M<-X/2
M## [,1] [,2] [,3] [,4]
## [1,] 0.5 -1.0 0 0.5
## [2,] 1.0 1.5 3 1.0
## [3,] -1.5 2.5 1 0.5
## [4,] 2.5 -1.0 2 2.0#20
B<-matrix(c(pi/3,(2/3)*pi,(2/3)*pi,pi),2)
B## [,1] [,2]
## [1,] 1.047198 2.094395
## [2,] 2.094395 3.141593sin(B)## [,1] [,2]
## [1,] 0.8660254 8.660254e-01
## [2,] 0.8660254 1.224606e-16cos(B)## [,1] [,2]
## [1,] 0.5 -0.5
## [2,] -0.5 -1.0tan(B)## [,1] [,2]
## [1,] 1.732051 -1.732051e+00
## [2,] -1.732051 -1.224647e-16#22
sqrt(B)## [,1] [,2]
## [1,] 1.023327 1.447203
## [2,] 1.447203 1.772454#23
exp(1)^B## [,1] [,2]
## [1,] 2.849654 8.120527
## [2,] 8.120527 23.140693#24
expm(B)## 2 x 2 Matrix of class "dsyMatrix"
## [,1] [,2]
## [1,] 23.9028 37.4119
## [2,] 37.4119 61.3147#26
#B<-matrix(c(pi/3,(2/3)*pi,(2/3)*pi,pi),2)
#logm(B)#28
4^B## [,1] [,2]
## [1,] 4.270471 18.23692
## [2,] 18.236920 77.88023#30
matrix(1,nrow = 2,ncol = 3)## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 1#32
matrix(c(1,0,0,1,0,0),2)## [,1] [,2] [,3]
## [1,] 1 0 0
## [2,] 0 1 0#34
matrix(0,nrow = 4,ncol = 4)## [,1] [,2] [,3] [,4]
## [1,] 0 0 0 0
## [2,] 0 0 0 0
## [3,] 0 0 0 0
## [4,] 0 0 0 0#36
a<-c(1,2,1,2,2,5,3,3,-3,2,7,-1,0,-3,-2,3)
C<-matrix(a,4)
t(C)## [,1] [,2] [,3] [,4]
## [1,] 1 2 1 2
## [2,] 2 5 3 3
## [3,] -3 2 7 -1
## [4,] 0 -3 -2 3#38
diag(C)## [1] 1 5 7 3#40
det(C)## [1] -13sum(diag(C))## [1] 16#Si se obtienen escalares, porque el determinante es un numero que caracteriza a una matriz y por ende se le atribuyen varias propiedades
#La traza de la matriz es la suma de los elentos de la diagonal, por ende se obtiene un escalar#41
C_1<-solve(C)#42
D<-C%*%C_1
D## [,1] [,2] [,3] [,4]
## [1,] 1.000000e+00 1.387779e-16 0 5.551115e-17
## [2,] -1.776357e-15 1.000000e+00 0 3.330669e-16
## [3,] 0.000000e+00 0.000000e+00 1 -5.551115e-17
## [4,] -8.881784e-16 0.000000e+00 0 1.000000e+00#Se obtiene la matriz identidad, sin embargo no se observa asi, porque al obtener la inversa y multiplicarlar por la original, se redondearon algunos valores, aqui se observa la matriz redondeada a enteros:
D<-round(D,2)
D## [,1] [,2] [,3] [,4]
## [1,] 1 0 0 0
## [2,] 0 1 0 0
## [3,] 0 0 1 0
## [4,] 0 0 0 1#44
eigen(C)## eigen() decomposition
## $values
## [1] 8.19439889+0.000000i 3.93791318+2.661524i 3.93791318-2.661524i
## [4] -0.07022524+0.000000i
##
## $vectors
## [,1] [,2] [,3] [,4]
## [1,] 0.24942346+0i 0.1235076+0.3224730i 0.1235076-0.3224730i 0.88639724+0i
## [2,] -0.41481971+0i 0.2577553+0.3723022i 0.2577553-0.3723022i -0.44089112+0i
## [3,] -0.87469708+0i 0.3369753-0.1771706i 0.3369753+0.1771706i 0.02228749+0i
## [4,] 0.02485078+0i 0.7285386+0.0000000i 0.7285386+0.0000000i -0.13934927+0i#46
rankMatrix(C)[1]## [1] 4#48
#B<-magic(7)
#B
#a<-NULL
#b<-NULL
#for (i in sequence(7)){
#a[i]<-sum(B[i,])
#b[i]<-sum(B[,i])
#}
#a
#b
#a y b son las sumas de cada fila y columna de la matriz B##Exercise 6
#2
# FUNCTION: volume(r)
#Este codigo obtiene el volumen de una esfera de radio 2
volume.m<-(4/3)*pi*(2^3)#4 example9
#este codigo genera un vector x tal que: x(n)=n^3
x<-NULL
for (n in sequence(7)){
x[n]<-n^3
}
x## [1] 1 8 27 64 125 216 343#6 example11
#este codigo genera un bucle, hasta que tol sea
tol=0
n=3
while (tol<1.5) {
n=n+1
tol=tol+0.1
}
n## [1] 18tol## [1] 1.5#8 price2(items)
price2<-0
for (items in c(2,4,6)){
if (items<3){
price2[items-1]<-items*130
}else if(items<5){
price2[items-2]<-items*160
}else if(items>5){
price2[items-3]<-items*200
}
}
price2## [1] 260 640 1200##Exercises 7
#1
x<-sequence(7)
y<-c(10,15,23,43,30,10,12)
plot(x,y,title('Exercise 2'),xlab = 'axisx',ylab = 'axisy')
#3
x<-(-6:6)
plot(x,y=(2*(x^3))+5,main = 'Exercise 3',xlab = 'x',ylab = 'y')
#4
x<-(-6:6)
plot(x,y=(2*(x^3))+5,main = 'Exercise 3',xlab = 'x',ylab = 'y',type='b', col='blue',pch=16,cex=1.5)
#6
x=sequence(10)
plot(x,2*(x^3)-4,type='b',col='green')
plot(x,x+1,type = 'b',col='red')
plot(x,2-sqrt(x),type = 'b',col='blue')
plot(x,(x^2)+3,type = 'b',col='yellow')
x<-(1:10)
y<-(1:10)
a<-function(x,y){
return(2*sin(x*y))
}
z<-outer(x,y,a)
op<-par(bg ='white')
persp(x,y,z,theta = 50,phi = 30,expand = 0.5,col = 'lightblue')
#x<-seq(0,4,length=25)
#y<-seq(0,4,length=25)
#a<-c(0.1,0.2,0.5,0.4,0.1,0.2,0.8,0.9,0.4,0.3,0.5,0.5,0.9,0.5,0.4,0.7,0.6,0.4,0.7,0.6,0.3,0.3,0.4,0.9,0.8)
#matrix(a,5)
#z<-outer(x,y,x)
#op<-par(bg='white')
#persp(x,y,z)