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3 and 4 .Determinants and Matrices
easy
निम्नलिखित सारणिकों के अवयवों के उपसारणिक एवं सहखंड लिखिए।:
$\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$
Option A
Option B
Option C
Option D
Solution
The given determinant is $\left|\begin{array}{ll}a & c \\ b & d\end{array}\right|$
Minor of element $a_{i j}$ is $M_{i j}$
$\therefore \mathrm{M}_{11}=$ minor of element $a_{11}=d$
$\mathrm{M}_{12}=$ minor of element $a_{12}=b$
$M_{21}=$ minor of element $a_{21}=c$
$\mathrm{M}_{22}=$ minor of element $a_{22}=a$
Cofactor of $a_{i j}$ is $A_{i j}=(-1)^{i+j} M_{i j}$
$\therefore A_{11}=(-1)^{1+1} M_{11}=(-1)^{2}(d)=d$
$A_{12}=(-1)^{1+2} M_{12}=(-1)^{3}(b)=-b$
$A_{21}=(-1)^{2+1} M_{21}=(-1)^{3}(c)=-c$
$A_{22}=(-1)^{2+2} M_{22}=(-1)^{4}(a)=a$
Standard 12
Mathematics
