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$3\displaystyle{n}$ ̐s $3\displaystyle{A}$

$3\displaystyle{\displaystyle{A=\left({\begin{array}\hspace{1}{a}_{11}&\cdots &\cdots &\hspace{1}{a}_{ 1n }& \vspace{6}\\ \vdots &\ddots & &\vdots & \vspace{6}\\ \vdots & &\ddots &\vdots & \vspace{6}\\ \hspace{1}{a}_{ n1 }&\cdots &\cdots &\hspace{1}{a}_{ nn }& \vspace{6}\\ \end{array}}\right)}}$

$3\displaystyle{\hspace{1}{a}_{ ij }}$ ]q( $3\displaystyle{\hspace{1}{A}_{ ij }}$ Ə)C

$3\displaystyle{\displaystyle{\hspace{1}{A}_{ ij }={ \( - 1 \) }^{ i+ j }\left|{\begin{array}\hspace{1}{a}_{11}&\cdots &\hspace{1}{a}_{ 1\(j- 1\) }&\hspace{1}{a}_{ 1\(j+ 1\) }&\cdots &\hspace{1}{a}_{ 1n }& \vspace{6}\\ \vdots & &\vdots &\vdots & & & \vspace{6}\\ \hspace{1}{a}_{ \(i- 1\)1 }&\cdots & & &\cdots &\hspace{1}{a}_{ \(i- 1\)1 }& \vspace{6}\\ \hspace{1}{a}_{ \(i+ 1\)1 }&\cdots & & &\cdots &\hspace{1}{a}_{ \(i+ 1\)1 }& \vspace{6}\\ \vdots & &\vdots &\vdots & & & \vspace{6}\\ \hspace{1}{a}_{ n1 }&\cdots &\hspace{1}{a}_{ n\(j- 1\) }&\hspace{1}{a}_{ n\(j+ 1\) }&\cdots &\hspace{1}{a}_{ nn }& \vspace{6}\\ \end{array}}\right|}}$

ƒ߂D܂C $3\displaystyle{A}$̍s$3\displaystyle{ \|A\| }$ $3\displaystyle{j}$ @ $3\displaystyle{\hspace{1}{a}_{ 1j }\hspace{5}\hspace{10} }$ ` $3\displaystyle{\hspace{1}{a}_{ nj }\hspace{5}\hspace{10} }$ ܂ł̗vfƁC $3\displaystyle{i}$ @s $3\displaystyle{\hspace{1}{a}_{ i1 }}$ ` $3\displaystyle{\hspace{1}{a}_{ in }}$ @܂ł̗vf폜 $3\displaystyle{ \( n- 1 \) }$ ̍s񎮂 $3\displaystyle{{ \( - 1 \) }^{ i+j }}$]qƂD

## ̗

$3\displaystyle{ A=\left({\begin{array}1&2&3& \vspace{6}\\ 4&5&6& \vspace{6}\\ 7&8&9& \vspace{6}\\ \end{array}}\right) }$

 $3\displaystyle{ \hspace{1}{A}_{11} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 1+1 }\left|{\begin{array}5&6& \vspace{6}\\ 8&9& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 5\times 9- 8\times 6 }\right) }$ $3\displaystyle{ =- 3 }$

 $3\displaystyle{ \hspace{1}{A}_{12} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 1+2 }\left|{\begin{array}4&6& \vspace{6}\\ 7&9& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 4\times 9- 7\times 6 }\right) }$ $3\displaystyle{ =- 6 }$

 $3\displaystyle{ \hspace{1}{A}_{13} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 1+3 }\left|{\begin{array}4&5& \vspace{6}\\ 7&8& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 4\times 8- 7\times 5 }\right) }$ $3\displaystyle{ =- 3 }$

 $3\displaystyle{ \hspace{1}{A}_{21} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 2+1 }\left|{\begin{array}2&3& \vspace{6}\\ 8&9& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 2\times 9- 8\times 3 }\right) }$ $3\displaystyle{ =- 6 }$

 $3\displaystyle{ \hspace{1}{A}_{22} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 2+2 }\left|{\begin{array}1&3& \vspace{6}\\ 7&9& \vspace{6}\\ \end{array}}\right| }$ $= 1 × 9 − 7 × 3$ $3\displaystyle{ =- 12 }$

 $3\displaystyle{ \hspace{1}{A}_{23} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 2+3 }\left|{\begin{array}1&2& \vspace{6}\\ 7&8& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 1\times 8- 7\times 2 }\right) }$ $3\displaystyle{ =- 6 }$

 $3\displaystyle{ \hspace{1}{A}_{31} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 3+1 }\left|{\begin{array}2&3& \vspace{6}\\ 5&6& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 2\times 6- 5\times 3 }\right) }$ $3\displaystyle{ =- 3 }$

 $3\displaystyle{ \hspace{1}{A}_{32} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 3+2 }\left|{\begin{array}1&3& \vspace{6}\\ 4&6& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 1\times 6- 4\times 3 }\right) }$ $3\displaystyle{ =- 6 }$

 $3\displaystyle{ \hspace{1}{A}_{33} }$ $3\displaystyle{ ={\left({ - 1 }\right)}^{ 3+3 }\left|{\begin{array}1&2& \vspace{6}\\ 4&5& \vspace{6}\\ \end{array}}\right| }$ $3\displaystyle{ =\left({ 1\times 5- 4\times 2 }\right) }$ $3\displaystyle{ =- 3 }$

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