Question

Write minors and cofactors of elements of following determinant. $\left|\begin{array}{cc}a& c\\ b& d\end{array}\right|$

Answer 1

Here, $\left|\begin{array}{cc}a& c\\ b& d\end{array}\right|\therefore$ Minors, $M_{11}=d,M_{12}=b,M_{21}=cand{M}_{22}=a$

Also cofactors, $A_{11}=(-1{)}^{1+1}{M}_{11}=1\times d=d{A}_{12}=(-1{)}^{1+2}{M}_{12}=(-1)\times b=-b{A}_{21}=(-1{)}^{2+1}{M}_{21}=(-1)\times c=-c{A}_{22}=(-1{)}^{2+2}{M}_{22}=1\times a=a$