Removing NAs from matrix

Hello R users,

I'm new to R so apologies if this question seems simple. I have a matrix which is 35000 columns by 35000 rows and I?m wanting to work out the mean of each row. I've tried using the code below on a smaller version of the matrix, but receive an error:

mat

       [,1]      [,2] [,3]      [,4]       [,5]      [,6]      [,7]      [,8]      [,9]     [,10]     [,11]
  [1,]   NA 0.3904762  0.2 0.4285714 0.04761905        NA        NA        NA        NA        NA        NA
  [2,]   NA        NA  0.2 0.2000000 0.23809524 0.2190476        NA        NA        NA        NA        NA
  [3,]   NA        NA   NA 0.5047619 0.27619048 0.2952381 0.1428571        NA        NA        NA        NA
  [4,]   NA        NA   NA        NA 0.42857143 0.3714286 0.3333333 0.2190476        NA        NA        NA
  [5,]   NA        NA   NA        NA         NA 0.8666667 0.6761905 0.4857143 0.6571429        NA        NA
  [6,]   NA        NA   NA        NA         NA        NA 0.6190476 0.4285714 0.6761905 0.4857143        NA
  [7,]   NA        NA   NA        NA         NA        NA        NA 0.6952381 0.6380952 0.6000000 0.2571429
  [8,]   NA        NA   NA        NA         NA        NA        NA        NA 0.6761905 0.6000000 0.1809524
  [9,]   NA        NA   NA        NA         NA        NA        NA        NA        NA 0.6190476 0.3142857
[10,]   NA        NA   NA        NA         NA        NA        NA        NA        NA        NA 0.5809524
[11,]   NA        NA   NA        NA         NA        NA        NA        NA        NA        NA        NA

mean.matrix <- matrix(ncol=1, nrow=10)
for (i in mat)

+ mean.matrix[,i] <- apply(mat,1,mean)
Error: NAs are not allowed in subscripted assignments

I have come across the na.omit() function however this completely removes the row. Is there any way I can either remove all the NAs from the matrix or pull out the values of each row to work out the mean?

Thanks,

Amie