Error with Generic Gaussian Elimination Code

I'm an R newbie and I'm trying to set up this simple Gaussian elimination code, but I keep receiving 2 errors and I'm not sure how to fix them.

Error 1: Error in a[i, j] <- a[i, j] - multiplier * a[k, j] :
replacement has length zero

Error 2: Error in a[i, j] : subscript out of bounds

Here's the code I have:


#Set Up Matrix
a <- matrix(c(0,2,3,2,1,1,5,1,0), byrow=T,nrow=3,ncol=3)
colnames(a) <- c("x","y","z")
k <- c(1,2,3)

b <- matrix(c(1,1,2),nrow = 3,ncol=1) 
rownames(b) <- c("i","j","k")
colnames(b) <- "b"
#Print a and b
a
b

#Row Counter
n <- nrow(a)


###### Forward Elimination ######

#Loop over all rows in matrix except last

  for (k in 1:n-1)
    {
#Loop over all rows below the diagonal position k,k
      
      for (i in k+1:n)
      {
       
      #Compute Multiplier for row i and column k
      multiplier = a[i,k]/a[k,k]
      
      #Loop over all columns to the right of the diagonal position k,k
      for (j in k + 1:n)
      {
        #Update coefficient for row i and column j
        a[i,j] = a[i,j] - multiplier * a[k,j]
      } 
      
      #Update right hand side for row i and column j
      b[i] = b[i] - multiplier*b[j]
    }
    }
###### Back Substitution ######
  #Loop backwards over all rows except last
      for (i in n:-1)
    {
      sum = 0
      
      #Loop over all columns to the right of the current row
      for (j in i+1:n)
      {
      sum = sum + a[i,j]*x[j]
      
        #Compute (i)th unknown
      x(i) = (b[i]- sum)/a[i,i]
      }
    }

Here is a resource for you on debugging.


probably the most relevant are the sections on print debugging, and interactive debugging (browser/debug etc)

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