Load data in the workspace by executing:

source("http://www3.nd.edu/~steve/computing_with_data_2014/9_Functions_matrices_lists/work_along_data_S9.R")

Compute the sums of the non-negative values of each column of mat2.

We can compute with these sums in one of two ways.
Method 1:

#Create vector for each column 
  col1 <- c(mat2[,1])
  col2 <- c(mat2[,2])
  col3 <- c(mat2[,3])
  col4 <- c(mat2[,4])
  col5 <- c(mat2[,5])
  col6 <- c(mat2[,6])
#Find non negative sums
  sum(col1[col1 > 0])
## [1] 0.2352207
  sum(col2[col2 > 0])
## [1] 0.1402782
  sum(col3[col3 > 0])
## [1] 3.037219
  sum(col4[col4 > 0])
## [1] 0.3641867
  sum(col5[col5 > 0])
## [1] 1.224913
  sum(col6[col6 > 0])
## [1] 3.507554

Alternatively, we can use the apply function to compute the sums in a more concise manner.
Method 2:

#Write a function that returns the sum of nonnegative numbers
  pos_sum <- function(x){
    sum(x[x > 0])
  }
  #With the defined function, we can drastically simplify nonnegative column sums
  col_pos_sums <- apply(mat2, 2, pos_sum) 
  col_pos_sums
## [1] 0.2352207 0.1402782 3.0372189 0.3641867 1.2249126 3.5075542