MATRICES

DEFINIR UNA MATRIZ Y CALCULAR SU TRANSPUESTA

B<-matrix(c(1,1,1,3,2,1,2,1,2),nrow = 3,ncol= 3)
Z<-t(B)
Z

##      [,1] [,2] [,3]
## [1,]    1    1    1
## [2,]    3    2    1
## [3,]    2    1    2

SISTEMAS DE ECUACIONES CON MATRICES

library(matlib)

## Warning: package 'matlib' was built under R version 3.6.2

A<-matrix(c(1,-2,5,-7), ncol = 2, nrow = 2)
b<- c(7,-5)
showEqn(A, b)

##  1*x1 + 5*x2  =   7 
## -2*x1 - 7*x2  =  -5

GRAFICAR EL SISTEMA DE ECUACIONES

A<-matrix(c(1,-2,5,-7), ncol = 2, nrow = 2)
b<- c(7,-5)
plotEqn(A,b, xlim=c(-10,0), labels=TRUE)

##    x1 + 5*x2  =   7 
## -2*x1 - 7*x2  =  -5

SOLUCION

A<-matrix(c(1,-2,5,-7), ncol = 2, nrow = 2)
b<- c(7,-5)
library(matlib)
Solve(A,b,verbose = TRUE, fractions = TRUE)

## 
## Initial matrix:
##      [,1] [,2] [,3]
## [1,]  1    5    7  
## [2,] -2   -7   -5  
## 
## row: 1 
## 
##  exchange rows 1 and 2 
##      [,1] [,2] [,3]
## [1,] -2   -7   -5  
## [2,]  1    5    7  
## 
##  multiply row 1 by -1/2 
##      [,1] [,2] [,3]
## [1,]   1  7/2  5/2 
## [2,]   1    5    7 
## 
##  subtract row 1 from row 2 
##      [,1] [,2] [,3]
## [1,]   1  7/2  5/2 
## [2,]   0  3/2  9/2 
## 
## row: 2 
## 
##  multiply row 2 by 2/3 
##      [,1] [,2] [,3]
## [1,]   1  7/2  5/2 
## [2,]   0    1    3 
## 
##  multiply row 2 by 7/2 and subtract from row 1 
##      [,1] [,2] [,3]
## [1,]  1    0   -8  
## [2,]  0    1    3  
## x1    =  -8 
##   x2  =   3

GRAFICAR MATRIZ CON TRES ECUACIONES

EL GRAFRICO SE OBSERVA EN UNA VENTANA APARTE, ES EN 3D

B<-matrix(c(1,2,3,1,4,6,2,-3,-5),ncol =3,nrow= 3)
c<- c(9,0,1)
library(matlib)
plotEqn3d(B,c)

REDUCCION GAUSSEANA

B<-matrix(c(1,3,2,1,2,1,1,1,2),ncol =3,nrow= 3)
c<- c(15,28,23)
library(matlib)
gaussianElimination(B,c,fractions = TRUE, verbose = TRUE)

## 
## Initial matrix:
##      [,1] [,2] [,3] [,4]
## [1,]  1    1    1   15  
## [2,]  3    2    1   28  
## [3,]  2    1    2   23  
## 
## row: 1 
## 
##  exchange rows 1 and 2 
##      [,1] [,2] [,3] [,4]
## [1,]  3    2    1   28  
## [2,]  1    1    1   15  
## [3,]  2    1    2   23  
## 
##  multiply row 1 by 1/3 
##      [,1] [,2] [,3] [,4]
## [1,]    1  2/3  1/3 28/3
## [2,]    1    1    1   15
## [3,]    2    1    2   23
## 
##  subtract row 1 from row 2 
##      [,1] [,2] [,3] [,4]
## [1,]    1  2/3  1/3 28/3
## [2,]    0  1/3  2/3 17/3
## [3,]    2    1    2   23
## 
##  multiply row 1 by 2 and subtract from row 3 
##      [,1] [,2] [,3] [,4]
## [1,]    1  2/3  1/3 28/3
## [2,]    0  1/3  2/3 17/3
## [3,]    0 -1/3  4/3 13/3
## 
## row: 2 
## 
##  multiply row 2 by 3 
##      [,1] [,2] [,3] [,4]
## [1,]    1  2/3  1/3 28/3
## [2,]    0    1    2   17
## [3,]    0 -1/3  4/3 13/3
## 
##  multiply row 2 by 2/3 and subtract from row 1 
##      [,1] [,2] [,3] [,4]
## [1,]    1    0   -1   -2
## [2,]    0    1    2   17
## [3,]    0 -1/3  4/3 13/3
## 
##  multiply row 2 by 1/3 and add to row 3 
##      [,1] [,2] [,3] [,4]
## [1,]  1    0   -1   -2  
## [2,]  0    1    2   17  
## [3,]  0    0    2   10  
## 
## row: 3 
## 
##  multiply row 3 by 1/2 
##      [,1] [,2] [,3] [,4]
## [1,]  1    0   -1   -2  
## [2,]  0    1    2   17  
## [3,]  0    0    1    5  
## 
##  multiply row 3 by 1 and add to row 1 
##      [,1] [,2] [,3] [,4]
## [1,]  1    0    0    3  
## [2,]  0    1    2   17  
## [3,]  0    0    1    5  
## 
##  multiply row 3 by 2 and subtract from row 2 
##      [,1] [,2] [,3] [,4]
## [1,] 1    0    0    3   
## [2,] 0    1    0    7   
## [3,] 0    0    1    5