#### Provide solution for RD Sharma maths class 12 chapter Determinants exercise 5.1 question 1 subquestion (ii)

$\mathrm{M}_{11}=3, \mathrm{M}_{21}=4, \mathrm{C}_{11}=3, \mathrm{C}_{21}=-4$

Hint:

Let Mij, Cij represents minor and cofactor of an element, where i and j represent the row and column. The minor of matrix can be obtained for particular element by removing the row and column where the element is present.

Given:

$A=\begin{bmatrix} -1 &4 \\ 2 &3 \end{bmatrix}$

Solution:

\begin{aligned} &\mathrm{M}_{11}=3 \\ &\mathrm{M}_{21}=4 \\ &\mathrm{C}_{\mathrm{ij}}=(-1)^{\mathrm{i}+j} \mathrm{M}_{\mathrm{ij}} \\ &\mathrm{C}_{11}=(-1)^{2} 3=3 \\ &\mathrm{C}_{21}=(-1)^{3} 4=-4 \\ &\mathrm{D}=(-1 \times 3)-(2 \times 4)=-3-8=-11 \end{aligned}