Find the minors and cofactors of all the elements of the determinant $\left|\begin{array}{rr}1 & -2 \\ 4 & 3\end{array}\right|$.
(N/A) The minor of the element $a_{ij}$ is denoted by $M_{ij}$.
For the given determinant $\left|\begin{array}{rr}1 & -2 \\ 4 & 3\end{array}\right|$:
$M_{11} = \text{Minor of } a_{11} = 3$
$M_{12} = \text{Minor of } a_{12} = 4$
$M_{21} = \text{Minor of } a_{21} = -2$
$M_{22} = \text{Minor of } a_{22} = 1$
The cofactor of the element $a_{ij}$ is denoted by $A_{ij} = (-1)^{i+j} M_{ij}$.
$A_{11} = (-1)^{1+1} M_{11} = (1)(3) = 3$
$A_{12} = (-1)^{1+2} M_{12} = (-1)(4) = -4$
$A_{21} = (-1)^{2+1} M_{21} = (-1)(-2) = 2$
$A_{22} = (-1)^{2+2} M_{22} = (1)(1) = 1$
For the given determinant $\left|\begin{array}{rr}1 & -2 \\ 4 & 3\end{array}\right|$:
$M_{11} = \text{Minor of } a_{11} = 3$
$M_{12} = \text{Minor of } a_{12} = 4$
$M_{21} = \text{Minor of } a_{21} = -2$
$M_{22} = \text{Minor of } a_{22} = 1$
The cofactor of the element $a_{ij}$ is denoted by $A_{ij} = (-1)^{i+j} M_{ij}$.
$A_{11} = (-1)^{1+1} M_{11} = (1)(3) = 3$
$A_{12} = (-1)^{1+2} M_{12} = (-1)(4) = -4$
$A_{21} = (-1)^{2+1} M_{21} = (-1)(-2) = 2$
$A_{22} = (-1)^{2+2} M_{22} = (1)(1) = 1$
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