SNair_Assign1Part2

write a function in Octave OR R that will take two variables (matrix A & constraint vector b) and solve using elimination.

Your function should produce the right answer for the system of equations for any 3-variable, 3-equation system.

You don’t have to worry about degenerate cases and can safely assume that the function will only be tested with a

system of equations that has a solution. Please note that you do have to worry about zero pivots, though.

Please test it with the system below and it should produce a solution x = [-1.55, -0.33, 0.95]

1 1 3

2 -1 5

-1 -2 4

x1

x2

x3

1

2

6

gaussian.elimination <- function(eq,sol)
{
  n <-nrow(eq)
  (eq.sol <-cbind(eq,sol))


  eq.sol[1,] <-eq.sol[1,]/eq.sol[1,1]

  for (i in 2:n)
     {
       for (j in i:n)
       {
         eq.sol[j, ] <- eq.sol[j, ] - eq.sol[i-1,] * eq.sol[j,i-1]
          
       }
       eq.sol[i,] <-eq.sol[i,]/eq.sol[i,i]
       
     }

  for (i in n:2)
  {
    for(j in i:2-1)
    {
      eq.sol[j,] <-eq.sol[j,] -eq.sol[i,] *eq.sol[j,i]
    }
  }
  eq.sol
  eq.sol[,4]
}

gaussian.elimination(matrix(c(1,1,3,2,-1,5,-1,-2,4),byrow=T,nrow=3,ncol=3),matrix(c(1,2,6),nrow=3,ncol=1))

## [1] -1.5454545 -0.3181818  0.9545455