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Align many matrices the best way possible?

TeX - LaTeX Asked by jubibanna on January 31, 2021

It’s my first assignment in linear algebra and working with matrices. How would you align matrices like below the best way?
enter image description here

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}

2 Answers

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}

enter image description here

Answered by user187802 on January 31, 2021

Another possible solution a bit more fast using spalign package:

enter image description here

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}

Answered by Sebastiano on January 31, 2021

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