Create new array from a fairly large first array efficiently

Dear, in R, I have a very large database and I want to create new columns. I will try to explain my problem with a very small matrix. Next, "1" means private school and "2", publishes. I have for example a database

>Data
Casa Escola 
 1     1
 1     1
 1     2
 1     2
 2     1
 2     2
 2     1
 3     1
 3     1
 3     1
 3     1

In this case, we conclude that house 1 has 4 residents who are in school, 2 in particular and 2 in public. Similarly, house 2 has 3 residents in school, 2 in particular and 1 in public. Finally, house 3 has 4 people in school and all in particular.

I want a new nuance with the first column indicating the house; the second indicating the number of children in the household; the third indicating the number of those who are in private school and Finally, the fourth, indicating the number of children in public school. Something like this:

  >matrix1
  >   Casa    em_escola     part     publ
       1          4          2        2
       2          3          2        1
       3          4          4        0

I've made a code that I'll show below. The problem with this code is that my original array is too large and takes hours to run. Also, I need to do the same thing for other arrays. Next, my code

lista1<- unique(Data$Casa)
length(lista1)
n=length(lista1)

lista_aux<- c(1:n)


matrix1<- data.frame(lista_aux,lista1)
nrow(matrix1)


for(i in 1:n) 
{


matrix = subset(Data , control_uc == lista1[i] )
matrix1$em_escola[i] <- nrow(matrix)

mat1<- subset (matrix, Escola == "1" )
matrix1$part[i]<- nrow(mat1)

mat2<- subset(matrix, cod_freq_escola =="2" )
matrix1$publ[i]<- nrow(mat2)
}