How to create a matrix of lists in R?

Question

What i want to have is a matrix in which each element is a list itself. See the following example:

Answer 1

This builds that matrix although the print method does not display it in the manner you imagined:

 matrix( list(c(1,2,4), c(NULL), c(1,2), c(3,4,5,6), c(1), c(1,3)), 2,3)
 #---------
     [,1]      [,2]      [,3]     
[1,] Numeric,3 Numeric,2 1        
[2,] NULL      Numeric,4 Numeric,2

Inspect the first element:

> Mlist <- matrix( list(c(1,2,4), c(NULL), c(1,2), c(3,4,5,6), c(1), c(1,3)), 2,3)
> Mlist[1,1]
[[1]]
[1] 1 2 4

> is.matrix(Mlist)
[1] TRUE
> class( Mlist[1,1] )
[1] "list"

Demonstration of creating "matrix of lists" from a list:

> will.become.a.matrix <- list(c(1,2,4), c(NULL), c(1,2), c(3,4,5,6), c(1), c(1,3))
> is.matrix(will.become.a.matrix)
[1] FALSE
> dim(will.become.a.matrix) <- c(2,3)
> is.matrix(will.become.a.matrix)
[1] TRUE
> dim(will.become.a.matrix)
[1] 2 3
> class(will.become.a.matrix[1,1])
[1] "list"

Further requested demonstration:

 A<- list(); F=list() E=list()
 A[1]<-c(3) ;  F[[1]]<-numeric(0);  E[[1]]<-numeric(0)
 A[2]<-c(1) ;  F[2]<-c(1)   ;        E[2]<-c(1)
 A[3]<-c(1) ;  F[3]<-c(2)  ;         E[[3]]<-numeric(0)
 A[[4]]<-list(1,3) ;F[[4]]<-numeric(0) ; E[[4]]<-numeric(0)
 A[5]<-c(4) ; F[5]<-c(4)       ;    E[5]<-c(4)
 Mlist= c(A,F,E)
 M <- matrix(Mlist, length(A), 3)
#=====================================
> M
     [,1]   [,2]      [,3]     
[1,] 3      Numeric,0 Numeric,0
[2,] 1      1         1        
[3,] 1      2         Numeric,0
[4,] List,2 Numeric,0 Numeric,0
[5,] 4      4         4        

You asked (in comments) "....is there a way to define number of column and rows , but not the element itself because they are unknown?"

Answered (initially in comments)

b<-matrix(rep(list(), 6),nrow = 2, ncol =3) 
#.... then replace the NULL items with values. 
# Need to use "[[": for assignment (which your 'Update 1' did not 
# ....and your Update2 only did for some but not all of the assignments.)

b[[1]] <- c(1,2,3,4)