Here is one way that will keep all the matrices together in a list
m <- matrix(1:12, 4)
lapply(seq_len(nrow(m)), function(i) matrix(m[1:i, ], ncol = ncol(m)))
#> [[1]]
#> [,1] [,2] [,3]
#> [1,] 1 5 9
#>
#> [[2]]
#> [,1] [,2] [,3]
#> [1,] 1 5 9
#> [2,] 2 6 10
#>
#> [[3]]
#> [,1] [,2] [,3]
#> [1,] 1 5 9
#> [2,] 2 6 10
#> [3,] 3 7 11
#>
#> [[4]]
#> [,1] [,2] [,3]
#> [1,] 1 5 9
#> [2,] 2 6 10
#> [3,] 3 7 11
#> [4,] 4 8 12
Created on 2020-10-16 by the reprex package (v0.3.0)