Question: Iteration

hello every body

  i wrote this code:

restart;

with(MmaTranslator[Mma]):
with(Student[NumericalAnalysis]):
with(DEtools, FunctionDecomposition):
with(linalg):with(ArrayTools):
with(LinearAlgebra):

n:=3 ;

  a:=(r)->q[r](t):
  x[1]:=Vector[row](n,a); 

  w[1]:=x[1];
                    
for j from 2 to 4 do
w[j]:= Vector[row]([w[j-1],x[j]]);  od;

 

i obtained the result so:::::::

                             x1:=[q1(t) q2(t) q3(t)]
                         w1:=[q1(t) q2(t) q3(t)]
                         w2:=[q1(t) q2(t) q3(t)  X2]
                         w3:=[q1(t) q2(t) q3(t)  X2  X3]
                         w4:=[q1(t) q2(t) q3(t)  X2  X3 X4]

  ::::::::::but I want the result in this form(only 2 components for each vector) :::::::
                          w2:=[w1   X2]
                          w3:=[w2   X3]
                          w4:=[w3   X4]
  how can solve I this problem           ?????? Note: x1,w1,w2,w3 and w4 are vectors.
                                                                                           x2,x3 and x4 are scalars
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