Find the Minors and Cofactor of each elements of the Determinant

• अवयव $a_{11} = 1$ के लिए: $M_{11} = \begin{vmatrix} 5 & -1 \\ 1 & 2 \end{vmatrix} = (5)(2) - (-1)(1) = 10 - (-1) = 11$

• अवयव $a_{12} = 0$ के लिए: $M_{12} = \begin{vmatrix} 3 & -1 \\ 0 & 2 \end{vmatrix} = (3)(2) - (-1)(0) = 6 - 0 = 6$

• अवयव $a_{13} = 4$ के लिए: $M_{13} = \begin{vmatrix} 3 & 5 \\ 0 & 1 \end{vmatrix} = (3)(1) - (5)(0) = 3 - 0 = 3$

• अवयव $a_{21} = 3$ के लिए: $M_{21} = \begin{vmatrix} 0 & 4 \\ 1 & 2 \end{vmatrix} = (0)(2) - (4)(1) = 0 - 4 = -4$

• अवयव $a_{22} = 5$ के लिए: $M_{22} = \begin{vmatrix} 1 & 4 \\ 0 & 2 \end{vmatrix} = (1)(2) - (4)(0) = 2 - 0 = 2$

• अवयव $a_{23} = -1$ के लिए: $M_{23} = \begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} = (1)(1) - (0)(0) = 1 - 0 = 1$

• अवयव $a_{31} = 0$ के लिए: $M_{31} = \begin{vmatrix} 0 & 4 \\ 5 & -1 \end{vmatrix} = (0)(-1) - (4)(5) = 0 - 20 = -20$

• अवयव $a_{32} = 1$ के लिए: $M_{32} = \begin{vmatrix} 1 & 4 \\ 3 & -1 \end{vmatrix} = (1)(-1) - (4)(3) = -1 - 12 = -13$

• अवयव $a_{33} = 2$ के लिए: $M_{33} = \begin{vmatrix} 1 & 0 \\ 3 & 5 \end{vmatrix} = (1)(5) - (0)(3) = 5 - 0 = 5$

• अवयव $a_{11} = 1$ के लिए: $C_{11} = (-1)^{1+1} M_{11} = (-1)^2 (11) = 1 \times 11 = 11$

• अवयव $a_{12} = 0$ के लिए: $C_{12} = (-1)^{1+2} M_{12} = (-1)^3 (6) = -1 \times 6 = -6$

• अवयव $a_{13} = 4$ के लिए: $C_{13} = (-1)^{1+3} M_{13} = (-1)^4 (3) = 1 \times 3 = 3$

• अवयव $a_{21} = 3$ के लिए: $C_{21} = (-1)^{2+1} M_{21} = (-1)^3 (-4) = -1 \times (-4) = 4$

• अवयव $a_{22} = 5$ के लिए: $C_{22} = (-1)^{2+2} M_{22} = (-1)^4 (2) = 1 \times 2 = 2$

• अवयव $a_{23} = -1$ के लिए: $C_{23} = (-1)^{2+3} M_{23} = (-1)^5 (1) = -1 \times 1 = -1$

• अवयव $a_{31} = 0$ के लिए: $C_{31} = (-1)^{3+1} M_{31} = (-1)^4 (-20) = 1 \times (-20) = -20$

• अवयव $a_{32} = 1$ के लिए: $C_{32} = (-1)^{3+2} M_{32} = (-1)^5 (-13) = -1 \times (-13) = 13$

• अवयव $a_{33} = 2$ के लिए: $C_{33} = (-1)^{3+3} M_{33} = (-1)^6 (5) = 1 \times 5 = 5$

अंतिम उत्तर:
प्रत्येक अवयव के माइनर और सहखंड इस प्रकार हैं:

• $a_{11} = 1$: $M_{11} = \boxed{\text{11}}$, $C_{11} = \boxed{\text{11}}$
• $a_{12} = 0$: $M_{12} = \boxed{\text{6}}$, $C_{12} = \boxed{\text{-6}}$
• $a_{13} = 4$: $M_{13} = \boxed{\text{3}}$, $C_{13} = \boxed{\text{3}}$
• $a_{21} = 3$: $M_{21} = \boxed{\text{-4}}$, $C_{21} = \boxed{\text{4}}$
• $a_{22} = 5$: $M_{22} = \boxed{\text{2}}$, $C_{22} = \boxed{\text{2}}$
• $a_{23} = -1$: $M_{23} = \boxed{\text{1}}$, $C_{23} = \boxed{\text{-1}}$
• $a_{31} = 0$: $M_{31} = \boxed{\text{-20}}$, $C_{31} = \boxed{\text{-20}}$
• $a_{32} = 1$: $M_{32} = \boxed{\text{-13}}$, $C_{32} = \boxed{\text{13}}$
• $a_{33} = 2$: $M_{33} = \boxed{\text{5}}$, $C_{33} = \boxed{\text{5}}$