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# Describe Minors And Cofactors

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## Minors And Cofactors:Minors and cofactors can be computed for each of the elements of a matrix. Minors: The minor of an element is equal to the determinant of the remaining elements of the matrix, after excluding the row and column containing the particular element. Cofactors: The cofactor of an element can be calculated from the minor of the element. The cofactor of an element is equal to the product of the minor of the element, and $-1$ to the power of position values of the row and column of the element.$\mathrm{Cofactor}\mathrm{of}\mathrm{an}\mathrm{Element}={\left(-1\right)}^{\mathrm{i}+\mathrm{j}}Ã—\mathrm{Minor}\mathrm{of}\mathrm{an}\mathrm{Element}$Here $iandj$are the positional values of the row and column of the element.exponent(power) of the sum of ${i}^{th}rowand{j}^{th}$ column containing the element.A = $\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$Thus, Minor of $a$ =$\left[\begin{array}{cc}e& f\\ h& i\end{array}\right]$The minor of the first element of the first row of the above matrix $A$ has been obtained after ignoring the first row and first column of the above matrix and forming a new matrix. Further, the cofactor of the element a is obtained by multiplying the minor with $\left(-1\right)$ to the power of the position value row and column of element $a$.$\mathrm{Cofactor}\mathrm{of}\mathrm{a}={\left(-1\right)}^{\mathrm{i}+\mathrm{j}}Ã—\mathrm{Minor}\mathrm{of}\mathrm{a}$Hence, $Cofactorofa={\left(-1\right)}^{1+1}Ã—\left[\begin{array}{cc}e& f\\ h& i\end{array}\right]$

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