Question #258645

Find the cofactor for given matrix 2575\begin{vmatrix} 2& 5\\ 7 & -5 \end{vmatrix}


1
Expert's answer
2021-11-03T17:36:50-0400

M1,1=(1)1+1(5)=5;M1,2=(1)1+27=7;M2,1=(1)2+15=5;M2,2=(1)2+22=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;\\

Cofactor(A)=(M1,1M1,2M2,1M2,2)\begin{pmatrix} M_{1,1} & M_{1,2}\\ M_{2,1} & M_{2,2} \end{pmatrix} =(5752)\begin{pmatrix} -5 & -7\\ -5 & 2 \end{pmatrix}


More explanations:

2575\begin{vmatrix} \colorbox{aqua}2 & \colorbox{aqua}5\\ \colorbox{aqua} 7 & -5 \end{vmatrix} M1,1=(1)1+1(5)=5M_{1,1}=(-1)^{1+1}\cdot (-5)=-5


257-5\begin{vmatrix} \colorbox{aqua}2 & \colorbox{aqua} 5\\ 7 &\colorbox{aqua} -5 \end{vmatrix} M1,2=(1)1+27=7M_{1,2}=(-1)^{1+2}\cdot 7=-7


257-5\begin{vmatrix} \colorbox{aqua}2 & 5\\ \colorbox{aqua}7 &\colorbox{aqua} -5 \end{vmatrix} M2,1=(1)2+15=5M_{2,1}=(-1)^{2+1}\cdot 5=-5


257-5\begin{vmatrix} 2 & \colorbox{aqua}5\\ \colorbox{aqua}7 &\colorbox{aqua} -5 \end{vmatrix} M2,2=(1)2+22=2;M_{2,2}=(-1)^{2+2}\cdot 2=2;


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