I try to loop trough a matrix but cant find a easy and elegant way instead of writing many (>10) equations… Can anyone help me please?

My Matrix looks like this:

and I want to calculate the following:

(0 * 0 * 4/24) + (0 * 1 * 6/24) + (0 * 2 * 3/24) + (1 * 0 * 3/24) + (1 * 1 * 4/24) + (1 * 2 * 4/24)

instead of using

__
btw: my code for the matrix

vals<- c(4/24, 6/24, 3/24, 3/24, 4/24, 4/24)
x <- c(0,1)
y <- c(0,1,2)
df <- matrix(vals, byrow = TRUE, nrow = 2, ncol = 3,
             dimnames = list(x,y))

instead of calculation each step manually, I think there should be a for-loop method, but cant figure it out..

>Solution :

x <- c(0, 1)
y <- c(0, 1, 2)
vals<- c(4/24, 6/24, 3/24, 3/24, 4/24, 4/24)
mat <- matrix(vals, byrow = TRUE, nrow = 2, ncol = 3,
              dimnames = list(x,y))  ## not a data frame; don't call it "df"

There is even a better way than a for loop:

sum(tcrossprod(x, y) * mat)
#[1] 0.5