R (programming language)/Tutorials/Linear algebra

Matrices: definition and multiplication

> b=matrix(nrow=2,ncol=2,c(1,2,3,4))
> a=matrix(nrow=2,ncol=2,c(1,0,0,-1))
> a
     [,1] [,2]
[1,]    1    0
[2,]    0   -1
> b
     [,1] [,2]
[1,]    1    3
[2,]    2    4
> a%*%b
     [,1] [,2]
[1,]    1    3
[2,]   -2   -4
> b%*%a
     [,1] [,2]
[1,]    1   -3
[2,]    2   -4
> 

Solving a linear equation

> m=matrix(nrow=2,ncol=2,c(1,-.8,1,.2))
> m
     [,1] [,2]
[1,]  1.0  1.0
[2,] -0.8  0.2
> 
> l=matrix(c(1.0+25.0/18,25.0/18.0))
> l
         [,1]
[1,] 2.388889
[2,] 1.388889
> 
> k=solve(m,l)
> k
           [,1]
[1,] -0.9111111
[2,]  3.3000000
> 
> m%*%k          #checking the answer
         [,1]
[1,] 2.388889
[2,] 1.388889
>