#### Please solve RD Sharma class 12 chapter Determinants exercise 5.1 question 1 subquestion (i) maths textbook solution

$\mathrm{M}_{11}=-1, \mathrm{M}_{21}=20, \mathrm{C}_{11}=-1, \mathrm{C}_{21}=-20$

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:

$A=\begin{bmatrix} 5 &20 \\ 0 &-1 \end{bmatrix}$

Solution:

\begin{aligned} &\mathrm{M}_{11}=-1 \\ &\mathrm{M}_{21}=20 \\ &\mathrm{C}_{\mathrm{ij}}=(-1)^{\mathrm{i}+\mathrm{j}} \mathrm{M}_{\mathrm{ij}} \\ &\mathrm{C}_{11}=(-1)^{2}(-1)=-1 \\ &\mathrm{C}_{21}=(-1)^{3}(20)=-20 \\ &\mathrm{D}=(-1 \times 5)-(20 \times 0)=-5 \end{aligned}