Matrix with top just top indexes

You can do that with nicematrix:

documentclass{article}
usepackage{nicematrix}

begin{document}

setcounter{MaxMatrixCols}{15}

$begin{bNiceMatrix}[first-row]
x & x^2 & x^3 & x^4 & x^5 & x^6 & x^7 & x^8 & x^9 & x^{10} 
r & -r  & 0     & 0    & 0     & 0     & 0      & 0      & 0    & 0    & ldots 
0 & r^2 & -2r^2 &      & 0     & 0     & 0      & 0      & 0    & 0    & ldots 
0 & r^3 & -3r^3 & 3r^3 & r^3   & 0     & 0      & 0      & 0    & 0    & ldots 
0 & 0   & 0     & r^4  & -4r^4 & 6r^4  & -4r^4  & r4     & 0    & 0    & ldots 
0 & 0   & 0     & 0    & r^5   & -5r^5 &  10r^5 & -10r^5 & 5r^5 & -r^5 & ldots 
vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots & ddots 
end{bNiceMatrix}$

end{document}

Just omit the final entries on each row in the blockarray that otherwise serve to label the rows (but do not omit the & preceding them.

To do a slightly simpler example than yours (since you didn't provide any source code, I didn't want to laboriously type all the entries of your 11-column matrix:

documentclass[11pt, a4paper]{article}
usepackage{amsmath,blkarray, bigstrut}

begin{document}

 [
     begin{blockarray}{*{5}{>{scriptstyle}c}}
       x & x^{2}& x^{3} &  
        begin{block}{[cccc] >{scriptstyle}c}
         bigstrut[t]  r & -r & 0 & cdots &          
          0 & r^{2} & -2 r^{2} & cdots & 
          0 & 0 & r^{3} & cdots & 
          0 & 0 & 0 & cdots & 
          vdots & vdots & vdots &ddots
        end{block}
      end{blockarray}
 ]

 end{document}