M 1 , 1 = ( − 1 ) 1 + 1 ⋅ ( − 5 ) = − 5 ; M 1 , 2 = ( − 1 ) 1 + 2 ⋅ 7 = − 7 ; M 2 , 1 = ( − 1 ) 2 + 1 ⋅ 5 = − 5 ; M 2 , 2 = ( − 1 ) 2 + 2 ⋅ 2 = 2 ; M_{1,1}=(-1)^{1+1}\cdot (-5)=-5;M_{1,2}=(-1)^{1+2}\cdot 7=-7;\\
M_{2,1}=(-1)^{2+1}\cdot 5=-5; M_{2,2}=(-1)^{2+2}\cdot 2=2;\\ M 1 , 1 = ( − 1 ) 1 + 1 ⋅ ( − 5 ) = − 5 ; M 1 , 2 = ( − 1 ) 1 + 2 ⋅ 7 = − 7 ; M 2 , 1 = ( − 1 ) 2 + 1 ⋅ 5 = − 5 ; M 2 , 2 = ( − 1 ) 2 + 2 ⋅ 2 = 2 ;
Cofactor(A)=( M 1 , 1 M 1 , 2 M 2 , 1 M 2 , 2 ) \begin{pmatrix}
M_{1,1} & M_{1,2}\\
M_{2,1} & M_{2,2}
\end{pmatrix} ( M 1 , 1 M 2 , 1 M 1 , 2 M 2 , 2 ) =( − 5 − 7 − 5 2 ) \begin{pmatrix}
-5 & -7\\
-5 & 2
\end{pmatrix} ( − 5 − 5 − 7 2 )
More explanations:
∣ 2 5 7 − 5 ∣ \begin{vmatrix}
\colorbox{aqua}2 & \colorbox{aqua}5\\
\colorbox{aqua} 7 & -5
\end{vmatrix} ∣ ∣ 2 7 5 − 5 ∣ ∣ M 1 , 1 = ( − 1 ) 1 + 1 ⋅ ( − 5 ) = − 5 M_{1,1}=(-1)^{1+1}\cdot (-5)=-5 M 1 , 1 = ( − 1 ) 1 + 1 ⋅ ( − 5 ) = − 5
∣ 2 5 7 - 5 ∣ \begin{vmatrix}
\colorbox{aqua}2 & \colorbox{aqua} 5\\
7 &\colorbox{aqua} -5
\end{vmatrix} ∣ ∣ 2 7 5 - 5 ∣ ∣ M 1 , 2 = ( − 1 ) 1 + 2 ⋅ 7 = − 7 M_{1,2}=(-1)^{1+2}\cdot 7=-7 M 1 , 2 = ( − 1 ) 1 + 2 ⋅ 7 = − 7
∣ 2 5 7 - 5 ∣ \begin{vmatrix}
\colorbox{aqua}2 & 5\\
\colorbox{aqua}7 &\colorbox{aqua} -5
\end{vmatrix} ∣ ∣ 2 7 5 - 5 ∣ ∣ M 2 , 1 = ( − 1 ) 2 + 1 ⋅ 5 = − 5 M_{2,1}=(-1)^{2+1}\cdot 5=-5 M 2 , 1 = ( − 1 ) 2 + 1 ⋅ 5 = − 5
∣ 2 5 7 - 5 ∣ \begin{vmatrix}
2 & \colorbox{aqua}5\\
\colorbox{aqua}7 &\colorbox{aqua} -5
\end{vmatrix} ∣ ∣ 2 7 5 - 5 ∣ ∣ M 2 , 2 = ( − 1 ) 2 + 2 ⋅ 2 = 2 ; M_{2,2}=(-1)^{2+2}\cdot 2=2; M 2 , 2 = ( − 1 ) 2 + 2 ⋅ 2 = 2 ;
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