Align many matrices the best way possible?

Question

It's my first assignment in linear algebra and working with matrices. How would you align matrices like below the best way?

Code below:

newenvironment{sysmatrix}[1]
 {left(begin{array}{@{}#1@{}}}
 {end{array}right)}
newcommand{ro}[1]{%
  xrightarrow{mathmakebox[rowidth]{#1}}%
}
newlength{rowidth}% row operation width
AtBeginDocument{setlength{rowidth}{4em}}

begin{equation}
  begin{array}{rcl}
  {
    left(!!!!
    begin{array}{rrr|r}
     1 &  a & 2 & a 
     0 &  1 & 0 & frac{-a^2}{a^2-2} 
     0 & 3-a & -2 & 2-a 
    end{array}
    !!right)
  } 
  & 
  xymatrix@C=15ex{ 
    ar[r]^-{small
      begin{array}{r}
        mathbf{r}_1 rightarrow mathbf{r}_1 - mathbf{r}_2a 
         mathbf{r}_3 rightarrow mathbf{r}_3 - mathbf{r}_2(3-a) 
      end{array}        
    } &
  } 
  & 
  {
    left(!!!!
    begin{array}{rrr|r}
     1  &  0 & 2 & -frac{2a}{a^2-2}  
     0 &  1 & 0 & frac{a^2}{a^2-2} 
     0 & 0 & -2 & frac{1}{a^2-2}(-a^2+2a-4)  
    end{array}
    !!right)
  } 
end{array}bigskip
end{equation}

begin{equation}
  begin{array}{rcl}
  {
    left(!!!!
    begin{array}{rrr|r}
     1  &  0 & 2 & -frac{2a}{a^2-2}  
     0 &  1 & 0 & frac{a^2}{a^2-2} 
     0 & 0 & -2 & frac{1}{a^2-2}(-a^2+2a-4)  
    end{array}
    !!right)
  } 
  & 
  xymatrix@C=16ex{ 
    ar[r]^-{small
      begin{array}{r}
         mathbf{r}_1 rightarrow mathbf{r}_1 + mathbf{r}_3 
         mathbf{r}_3 rightarrow frac{mathbf{r}_3}{-2}
      end{array}        
    } &
  } 
  & 
  {
    left(!!!!
    begin{array}{rrr|r}
     1 &  0 & 0 & -frac{a^2+4}{a^2-2}  
     0 &  1 & 0 & frac{a^2}{a^2-2} 
     0 &  0 & 1 & frac{frac{a^2}{2}-a+2}{a^2-2}
    end{array}
    !!right)
  } 
end{array}
end{equation}

user187802 · Answer

documentclass[a4paper]{article}
usepackage[margin=2cm]{geometry}
usepackage{array}
usepackage{amsmath}
begin{document}

begin{align}
    left(begin{array}{ccc|>{displaystyle}c}
    1 &  a & 2 & a 
    0 &  1 & 0 & frac{-a^2}{a^2-2} 
    0 & 3-a & -2 & 2-a 
    end{array}right) 
& xrightarrow{small
        begin{array}{r}
        mathbf{r}_1 rightarrow mathbf{r}_1 - mathbf{r}_2a 
        mathbf{r}_3 rightarrow mathbf{r}_3 - mathbf{r}_2(3-a) 
        end{array}} 
    left(begin{array}{ccc|>{displaystyle}c}
    1  &  0 & 2 & -frac{2a}{a^2-2}  
    0 &  1 & 0 & frac{a^2}{a^2-2} 
    0 & 0 & -2 & frac{1}{a^2-2}(-a^2+2a-4)  
    end{array}right)  [10pt]
left(begin{array}{rrr|>{displaystyle}r}
    1  &  0 & 2 & -frac{2a}{a^2-2}  
    0 &  1 & 0 & frac{a^2}{a^2-2} 
    0 & 0 & -2 & frac{1}{a^2-2}(-a^2+2a-4)  
    end{array}right)
&  xrightarrow[hphantom{textstyle~mathbf{r}_3 rightarrow mathbf{r}_3 - mathbf{r}_2(3-a)}]%
      {small
        begin{array}{r}
        mathbf{r}_1 rightarrow mathbf{r}_1 + mathbf{r}_3 
        mathbf{r}_3 rightarrow frac{mathbf{r}_3}{-2}
        end{array}}
left(begin{array}{rrr|>{displaystyle}r}
    1 &  0 & 0 & -frac{a^2+4}{a^2-2}  
    0 &  1 & 0 & frac{a^2}{a^2-2} 
    0 &  0 & 1 & frac{frac{a^2}{2}-a+2}{a^2-2}
    end{array}right) 
end{align}

end{document}

Sebastiano · Answer

Another possible solution a bit more fast using spalign package:

documentclass[a4paper,12pt]{article}
usepackage[margin=2.2cm]{geometry}
usepackage{mathtools}
usepackage{spalign}

begin{document}
begin{equation}
spalignaugmat[c]{1 a 2 a; 0 1 0 dfrac{-a^2}{a^2-2}; 0 3-a -2 2-a} xrightarrow{begin{matrix}
mathbf{r}_1 rightarrow mathbf{r}_1 - mathbf{r}_2a 
        mathbf{r}_3 rightarrow mathbf{r}_3 - mathbf{r}_2(3-a) 
end{matrix}}{} 
  spalignaugmat{1 0 2 -dfrac{2a}{a^2-2}; 0 1 0 dfrac{a^2}{a^2-2}; 0 0 -2 dfrac{1}{a^2-2}(-a^2+2a-4)}    
end{equation}

begin{equation}
spalignaugmat[c]{1 0 2 -dfrac{2a}{a^2-2}; 0 1 0  dfrac{a^2}{a^2-2}; 0 0 -2 dfrac{1}{a^2-2}(-a^2+2a-4)} xrightarrow{begin{matrix}
mathbf{r}_1 rightarrow mathbf{r}_1 + mathbf{r}_3 
        mathbf{r}_3 rightarrow -frac{1}{2}mathbf{r}_3
end{matrix}}{}    
  spalignaugmat{1 0 0 -dfrac{a^2+4}{a^2-2}; 0 1 0 dfrac{a^2}{a^2-2}; 0 0 1 dfrac{frac{a^2}{2}-a+2}{a^2-2}}    
end{equation}
[mathbf{S}^{ast}=spalignaugmat[c]{1 0 0 -frac{a^2+4}{a^2-2};0 1 0 frac{a^2}{a^2-2};  0 0 1 frac{frac{a^2}{2}-a+2}{a^2-2}}]

end{document}

Align many matrices the best way possible?

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