Determinant of 3x3 matrix by cofactor expansion

please help me to create this in LaTeX:

enter image description here

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

asked Feb 22 at 12:49

Said

252

add a comment |

please help me to create this in LaTeX:

enter image description here

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

asked Feb 22 at 12:49

Said

252

add a comment |

please help me to create this in LaTeX:

enter image description here

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

asked Feb 22 at 12:49

Said

252

please help me to create this in LaTeX:

enter image description here

matrices tikz-matrix

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

asked Feb 22 at 12:49

Said

252

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

asked Feb 22 at 12:49

Said

252

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

edited Feb 22 at 12:49

Phelype Oleinik

23.6k54586

asked Feb 22 at 12:49

Said

252

asked Feb 22 at 12:49

Said

252

asked Feb 22 at 12:49

Said

252

add a comment |

3 Answers
3

active

oldest

votes

A simple code with pstricks and mathtools:

documentclass[svgnames]{article}

usepackage{mathtools} 

usepackage{pst-node, auto-pst-pdf}



begin{document}



begin{postscript}

psset{{linecolor=DeepPink}, framesep=2pt, nodesepB=-8pt}

[ begin{bmatrix}

mathclap{circlenode[linestyle=dashed, dash=3.5pt 2.5pt]{A}{0}} & 2 & rnode{C}{1} \

3 & -1 & 2 \

rnode{B}{4} & 0 & 1 

end{bmatrix} ]

ncline{A}{B}

ncline{A}{C}

end{postscript}



end{document}

enter image description here

edited Feb 22 at 21:59

answered Feb 22 at 13:48

Bernard

171k775203

Thanks alot Bernard.

– Said
Feb 22 at 14:01

add a comment |

documentclass{article}

usepackage{tikz}

usetikzlibrary{fit}



newcommand{tikzmark}[2]{tikz[overlay,remember picture,baseline=(#1.base)] node (#1) {#2};}



begin{document}

[

 left[begin{array}{*3{c}}

    tikzmark{left_end}{0} & 2 & tikzmark{right_end}{1}\

    3 & -1 & 2 \

    tikzmark{down_left}{4} & 0 & tikzmark{down}{1}

  end{array}right]

]

tikz[overlay,remember picture] {

draw[red,thick,dashed] (left_end) circle (0.2cm);

    draw[-,red,thick] (left_end) -- ++ (1.7,0) (right_end);

    draw[-,red,thick] (left_end) -- ++ (0,-1.) (down_left);

}

end{document}

enter image description here

answered Feb 22 at 13:23

Sina Ahmadi

77338

Thanks alot Sina Ahmadi.

– Said
Feb 22 at 14:00

@Said Please mark it as an answer to close your question.

– Sina Ahmadi
Feb 22 at 14:34

I posted some extended comments below. If you address them in your answer, I will be happy to remove them.

– marmot
Feb 22 at 16:00

Thanks @marmot. Interesting comments and smoother solution.

– Sina Ahmadi
Feb 22 at 16:05

You can really take them over, I do not want to post an answer here. I just want to avoid that tikzmark gets redefined.

– marmot
Feb 22 at 16:07

add a comment |

This is more an extended comment on the answer by Sina Ahmadi. I will be happy to remove this if in that answer a few things get changed.

tikzmark is a phantastic command that is part of the tikzmark library. I would like to argue that creating a new command with this name is not a good practice.

The nodes right_end and down_left are not used. The lines are drawn as determined by the two hard-coded distances - ++ (1.7,0) and - ++ (0,-1.).

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}



begin{document}

[begin{bmatrix}

    tikzmarknode[circle,draw=red,inner sep=0.5pt,densely dashed]{A11}{0} & 2 & tikzmarknode{A13}{1}\

    3 & -1 & 2 \

    tikzmarknode{A31}{4} & 0 & 1

 end{bmatrix} 

]

begin{tikzpicture}[overlay,remember picture] 

draw[red] (A11.east) -- (A11.east-|A13.east)

(A11.south) -- (A11.south|-A31.south);

end{tikzpicture}

end{document}

enter image description here

answered Feb 22 at 15:59

marmot

105k4124236

Thank you very much marmot.

– Said
Feb 22 at 21:53

@Said You're welcome! (BTW, you can only accept one answer. Given that you accepted Sina's answer first, you might want to place the tick there.)

– marmot
Feb 22 at 22:04

add a comment |

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3 Answers
3

active

oldest

votes

3 Answers
3

active

oldest

votes

A simple code with pstricks and mathtools:

documentclass[svgnames]{article}

usepackage{mathtools} 

usepackage{pst-node, auto-pst-pdf}



begin{document}



begin{postscript}

psset{{linecolor=DeepPink}, framesep=2pt, nodesepB=-8pt}

[ begin{bmatrix}

mathclap{circlenode[linestyle=dashed, dash=3.5pt 2.5pt]{A}{0}} & 2 & rnode{C}{1} \

3 & -1 & 2 \

rnode{B}{4} & 0 & 1 

end{bmatrix} ]

ncline{A}{B}

ncline{A}{C}

end{postscript}



end{document}

enter image description here

edited Feb 22 at 21:59

answered Feb 22 at 13:48

Bernard

171k775203

Thanks alot Bernard.

– Said
Feb 22 at 14:01

add a comment |

A simple code with pstricks and mathtools:

documentclass[svgnames]{article}

usepackage{mathtools} 

usepackage{pst-node, auto-pst-pdf}



begin{document}



begin{postscript}

psset{{linecolor=DeepPink}, framesep=2pt, nodesepB=-8pt}

[ begin{bmatrix}

mathclap{circlenode[linestyle=dashed, dash=3.5pt 2.5pt]{A}{0}} & 2 & rnode{C}{1} \

3 & -1 & 2 \

rnode{B}{4} & 0 & 1 

end{bmatrix} ]

ncline{A}{B}

ncline{A}{C}

end{postscript}



end{document}

enter image description here

edited Feb 22 at 21:59

answered Feb 22 at 13:48

Bernard

171k775203

Thanks alot Bernard.

– Said
Feb 22 at 14:01

add a comment |

A simple code with pstricks and mathtools:

documentclass[svgnames]{article}

usepackage{mathtools} 

usepackage{pst-node, auto-pst-pdf}



begin{document}



begin{postscript}

psset{{linecolor=DeepPink}, framesep=2pt, nodesepB=-8pt}

[ begin{bmatrix}

mathclap{circlenode[linestyle=dashed, dash=3.5pt 2.5pt]{A}{0}} & 2 & rnode{C}{1} \

3 & -1 & 2 \

rnode{B}{4} & 0 & 1 

end{bmatrix} ]

ncline{A}{B}

ncline{A}{C}

end{postscript}



end{document}

enter image description here

edited Feb 22 at 21:59

answered Feb 22 at 13:48

Bernard

171k775203

A simple code with pstricks and mathtools:

documentclass[svgnames]{article}

usepackage{mathtools} 

usepackage{pst-node, auto-pst-pdf}



begin{document}



begin{postscript}

psset{{linecolor=DeepPink}, framesep=2pt, nodesepB=-8pt}

[ begin{bmatrix}

mathclap{circlenode[linestyle=dashed, dash=3.5pt 2.5pt]{A}{0}} & 2 & rnode{C}{1} \

3 & -1 & 2 \

rnode{B}{4} & 0 & 1 

end{bmatrix} ]

ncline{A}{B}

ncline{A}{C}

end{postscript}



end{document}

enter image description here

edited Feb 22 at 21:59

answered Feb 22 at 13:48

Bernard

171k775203

edited Feb 22 at 21:59

answered Feb 22 at 13:48

Bernard

171k775203

answered Feb 22 at 13:48

Bernard

171k775203

answered Feb 22 at 13:48

Bernard

171k775203

Thanks alot Bernard.

– Said
Feb 22 at 14:01

add a comment |

Thanks alot Bernard.

– Said
Feb 22 at 14:01

Thanks alot Bernard.

– Said
Feb 22 at 14:01

add a comment |

documentclass{article}

usepackage{tikz}

usetikzlibrary{fit}



newcommand{tikzmark}[2]{tikz[overlay,remember picture,baseline=(#1.base)] node (#1) {#2};}



begin{document}

[

 left[begin{array}{*3{c}}

    tikzmark{left_end}{0} & 2 & tikzmark{right_end}{1}\

    3 & -1 & 2 \

    tikzmark{down_left}{4} & 0 & tikzmark{down}{1}

  end{array}right]

]

tikz[overlay,remember picture] {

draw[red,thick,dashed] (left_end) circle (0.2cm);

    draw[-,red,thick] (left_end) -- ++ (1.7,0) (right_end);

    draw[-,red,thick] (left_end) -- ++ (0,-1.) (down_left);

}

end{document}

enter image description here

answered Feb 22 at 13:23

Sina Ahmadi

77338

Thanks alot Sina Ahmadi.

– Said
Feb 22 at 14:00

@Said Please mark it as an answer to close your question.

– Sina Ahmadi
Feb 22 at 14:34

I posted some extended comments below. If you address them in your answer, I will be happy to remove them.

– marmot
Feb 22 at 16:00

Thanks @marmot. Interesting comments and smoother solution.

– Sina Ahmadi
Feb 22 at 16:05

You can really take them over, I do not want to post an answer here. I just want to avoid that tikzmark gets redefined.

– marmot
Feb 22 at 16:07

add a comment |

documentclass{article}

usepackage{tikz}

usetikzlibrary{fit}



newcommand{tikzmark}[2]{tikz[overlay,remember picture,baseline=(#1.base)] node (#1) {#2};}



begin{document}

[

 left[begin{array}{*3{c}}

    tikzmark{left_end}{0} & 2 & tikzmark{right_end}{1}\

    3 & -1 & 2 \

    tikzmark{down_left}{4} & 0 & tikzmark{down}{1}

  end{array}right]

]

tikz[overlay,remember picture] {

draw[red,thick,dashed] (left_end) circle (0.2cm);

    draw[-,red,thick] (left_end) -- ++ (1.7,0) (right_end);

    draw[-,red,thick] (left_end) -- ++ (0,-1.) (down_left);

}

end{document}

enter image description here

answered Feb 22 at 13:23

Sina Ahmadi

77338

Thanks alot Sina Ahmadi.

– Said
Feb 22 at 14:00

@Said Please mark it as an answer to close your question.

– Sina Ahmadi
Feb 22 at 14:34

I posted some extended comments below. If you address them in your answer, I will be happy to remove them.

– marmot
Feb 22 at 16:00

Thanks @marmot. Interesting comments and smoother solution.

– Sina Ahmadi
Feb 22 at 16:05

You can really take them over, I do not want to post an answer here. I just want to avoid that tikzmark gets redefined.

– marmot
Feb 22 at 16:07

add a comment |

documentclass{article}

usepackage{tikz}

usetikzlibrary{fit}



newcommand{tikzmark}[2]{tikz[overlay,remember picture,baseline=(#1.base)] node (#1) {#2};}



begin{document}

[

 left[begin{array}{*3{c}}

    tikzmark{left_end}{0} & 2 & tikzmark{right_end}{1}\

    3 & -1 & 2 \

    tikzmark{down_left}{4} & 0 & tikzmark{down}{1}

  end{array}right]

]

tikz[overlay,remember picture] {

draw[red,thick,dashed] (left_end) circle (0.2cm);

    draw[-,red,thick] (left_end) -- ++ (1.7,0) (right_end);

    draw[-,red,thick] (left_end) -- ++ (0,-1.) (down_left);

}

end{document}

enter image description here

answered Feb 22 at 13:23

Sina Ahmadi

77338

documentclass{article}

usepackage{tikz}

usetikzlibrary{fit}



newcommand{tikzmark}[2]{tikz[overlay,remember picture,baseline=(#1.base)] node (#1) {#2};}



begin{document}

[

 left[begin{array}{*3{c}}

    tikzmark{left_end}{0} & 2 & tikzmark{right_end}{1}\

    3 & -1 & 2 \

    tikzmark{down_left}{4} & 0 & tikzmark{down}{1}

  end{array}right]

]

tikz[overlay,remember picture] {

draw[red,thick,dashed] (left_end) circle (0.2cm);

    draw[-,red,thick] (left_end) -- ++ (1.7,0) (right_end);

    draw[-,red,thick] (left_end) -- ++ (0,-1.) (down_left);

}

end{document}

enter image description here

answered Feb 22 at 13:23

Sina Ahmadi

77338

answered Feb 22 at 13:23

Sina Ahmadi

77338

answered Feb 22 at 13:23

Sina Ahmadi

77338

answered Feb 22 at 13:23

Sina Ahmadi

77338

Thanks alot Sina Ahmadi.

– Said
Feb 22 at 14:00

@Said Please mark it as an answer to close your question.

– Sina Ahmadi
Feb 22 at 14:34

I posted some extended comments below. If you address them in your answer, I will be happy to remove them.

– marmot
Feb 22 at 16:00

Thanks @marmot. Interesting comments and smoother solution.

– Sina Ahmadi
Feb 22 at 16:05

You can really take them over, I do not want to post an answer here. I just want to avoid that tikzmark gets redefined.

– marmot
Feb 22 at 16:07

add a comment |

Thanks alot Sina Ahmadi.

– Said
Feb 22 at 14:00

@Said Please mark it as an answer to close your question.

– Sina Ahmadi
Feb 22 at 14:34

I posted some extended comments below. If you address them in your answer, I will be happy to remove them.

– marmot
Feb 22 at 16:00

Thanks @marmot. Interesting comments and smoother solution.

– Sina Ahmadi
Feb 22 at 16:05

You can really take them over, I do not want to post an answer here. I just want to avoid that tikzmark gets redefined.

– marmot
Feb 22 at 16:07

Thanks alot Sina Ahmadi.

– Said
Feb 22 at 14:00

@Said Please mark it as an answer to close your question.

– Sina Ahmadi
Feb 22 at 14:34

I posted some extended comments below. If you address them in your answer, I will be happy to remove them.

– marmot
Feb 22 at 16:00

Thanks @marmot. Interesting comments and smoother solution.

– Sina Ahmadi
Feb 22 at 16:05

You can really take them over, I do not want to post an answer here. I just want to avoid that tikzmark gets redefined.

– marmot
Feb 22 at 16:07

add a comment |

This is more an extended comment on the answer by Sina Ahmadi. I will be happy to remove this if in that answer a few things get changed.

tikzmark is a phantastic command that is part of the tikzmark library. I would like to argue that creating a new command with this name is not a good practice.

The nodes right_end and down_left are not used. The lines are drawn as determined by the two hard-coded distances - ++ (1.7,0) and - ++ (0,-1.).

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}



begin{document}

[begin{bmatrix}

    tikzmarknode[circle,draw=red,inner sep=0.5pt,densely dashed]{A11}{0} & 2 & tikzmarknode{A13}{1}\

    3 & -1 & 2 \

    tikzmarknode{A31}{4} & 0 & 1

 end{bmatrix} 

]

begin{tikzpicture}[overlay,remember picture] 

draw[red] (A11.east) -- (A11.east-|A13.east)

(A11.south) -- (A11.south|-A31.south);

end{tikzpicture}

end{document}

enter image description here

answered Feb 22 at 15:59

marmot

105k4124236

Thank you very much marmot.

– Said
Feb 22 at 21:53

@Said You're welcome! (BTW, you can only accept one answer. Given that you accepted Sina's answer first, you might want to place the tick there.)

– marmot
Feb 22 at 22:04

add a comment |

This is more an extended comment on the answer by Sina Ahmadi. I will be happy to remove this if in that answer a few things get changed.

tikzmark is a phantastic command that is part of the tikzmark library. I would like to argue that creating a new command with this name is not a good practice.

The nodes right_end and down_left are not used. The lines are drawn as determined by the two hard-coded distances - ++ (1.7,0) and - ++ (0,-1.).

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}



begin{document}

[begin{bmatrix}

    tikzmarknode[circle,draw=red,inner sep=0.5pt,densely dashed]{A11}{0} & 2 & tikzmarknode{A13}{1}\

    3 & -1 & 2 \

    tikzmarknode{A31}{4} & 0 & 1

 end{bmatrix} 

]

begin{tikzpicture}[overlay,remember picture] 

draw[red] (A11.east) -- (A11.east-|A13.east)

(A11.south) -- (A11.south|-A31.south);

end{tikzpicture}

end{document}

enter image description here

answered Feb 22 at 15:59

marmot

105k4124236

Thank you very much marmot.

– Said
Feb 22 at 21:53

@Said You're welcome! (BTW, you can only accept one answer. Given that you accepted Sina's answer first, you might want to place the tick there.)

– marmot
Feb 22 at 22:04

add a comment |

This is more an extended comment on the answer by Sina Ahmadi. I will be happy to remove this if in that answer a few things get changed.

tikzmark is a phantastic command that is part of the tikzmark library. I would like to argue that creating a new command with this name is not a good practice.

The nodes right_end and down_left are not used. The lines are drawn as determined by the two hard-coded distances - ++ (1.7,0) and - ++ (0,-1.).

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}



begin{document}

[begin{bmatrix}

    tikzmarknode[circle,draw=red,inner sep=0.5pt,densely dashed]{A11}{0} & 2 & tikzmarknode{A13}{1}\

    3 & -1 & 2 \

    tikzmarknode{A31}{4} & 0 & 1

 end{bmatrix} 

]

begin{tikzpicture}[overlay,remember picture] 

draw[red] (A11.east) -- (A11.east-|A13.east)

(A11.south) -- (A11.south|-A31.south);

end{tikzpicture}

end{document}

enter image description here

answered Feb 22 at 15:59

marmot

105k4124236

This is more an extended comment on the answer by Sina Ahmadi. I will be happy to remove this if in that answer a few things get changed.

tikzmark is a phantastic command that is part of the tikzmark library. I would like to argue that creating a new command with this name is not a good practice.

The nodes right_end and down_left are not used. The lines are drawn as determined by the two hard-coded distances - ++ (1.7,0) and - ++ (0,-1.).

documentclass{article}

usepackage{amsmath}

usepackage{tikz}

usetikzlibrary{tikzmark}



begin{document}

[begin{bmatrix}

    tikzmarknode[circle,draw=red,inner sep=0.5pt,densely dashed]{A11}{0} & 2 & tikzmarknode{A13}{1}\

    3 & -1 & 2 \

    tikzmarknode{A31}{4} & 0 & 1

 end{bmatrix} 

]

begin{tikzpicture}[overlay,remember picture] 

draw[red] (A11.east) -- (A11.east-|A13.east)

(A11.south) -- (A11.south|-A31.south);

end{tikzpicture}

end{document}

enter image description here

answered Feb 22 at 15:59

marmot

105k4124236

answered Feb 22 at 15:59

marmot

105k4124236

answered Feb 22 at 15:59

marmot

105k4124236

answered Feb 22 at 15:59

marmot

105k4124236

Thank you very much marmot.

– Said
Feb 22 at 21:53

@Said You're welcome! (BTW, you can only accept one answer. Given that you accepted Sina's answer first, you might want to place the tick there.)

– marmot
Feb 22 at 22:04

add a comment |

Thank you very much marmot.

– Said
Feb 22 at 21:53

@Said You're welcome! (BTW, you can only accept one answer. Given that you accepted Sina's answer first, you might want to place the tick there.)

– marmot
Feb 22 at 22:04

Thank you very much marmot.

– Said
Feb 22 at 21:53

@Said You're welcome! (BTW, you can only accept one answer. Given that you accepted Sina's answer first, you might want to place the tick there.)

– marmot
Feb 22 at 22:04

add a comment |

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