Linear Algebra in R

By admin on October 21, 2019

Linear algebra is a branch of mathematics that consists of a set of tools to solve equations like this -

7x + 2y = 13
4x -  y =  1

We will use the R package “matlib” for this purpose. Install it, if you do not have it yet, and then load the library. This package gives you a number of functions for solving linear equations.

library(matlib)

The function ‘matrix’ allows you to turn a vector into matrix. This package gives you a number of functions for solving linear equations.

A = matrix(1:10, nrow=2, ncol=5, byrow=TRUE)
A = matrix(1:10, nrow=2, ncol=5, byrow=FALSE)

To solve the equation, we will create matrix with numbers, apply matlib functions ‘showEqn’ to make sure the equation is correct and then ‘Solve’.

A <- matrix(c(7,4,2,-1),2,2)
b <- c(13,1)
#
#
showEqn(A,b)

## 7*x1 + 2*x2  =  13 
## 4*x1 - 1*x2  =   1

Solve(A,b)

## x1    =  1 
##   x2  =  3

Solve(A,b,fractions=TRUE)

## x1    =  1 
##   x2  =  3

Let us have a bit more practice with another equation -

3x + 7y =  3
4x - 5y = -5

A <-matrix(c(3,4,7,-5),2,2)
b <- c(3,-5)
#
#
showEqn(A,b)

## 3*x1 + 7*x2  =   3 
## 4*x1 - 5*x2  =  -5

Solve(A,b,fractions=TRUE)

## x1    =  -20/43 
##   x2  =   27/43

Here is a three variable equation.

x  + 7y + z  = 30
2x -  y - z  =  5
x  -  y +3z  = 12

A <-matrix(c(1,2,1,7,-1,-1,1,-1,3),3,3)
b <- c(30,5,12)
#
#
showEqn(A,b)

## 1*x1 + 7*x2 + 1*x3  =  30 
## 2*x1 - 1*x2 - 1*x3  =   5 
## 1*x1 - 1*x2 + 3*x3  =  12

Solve(A,b,fractions=TRUE)

## x1      =  151/27 
##   x2    =   82/27 
##     x3  =   85/27