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 >