Relations — Maths STD 12 Science — Question

On expanding by first row, the value of the determinant of 3 × 3 square matrix A = [a_ij] is a₁₁ C₁₁ + a₁₂ C₁₂ + a₁₃ C₁₃, where [C_ij] is the cofactor of a_ij in A. Write the expression for its value on expanding by second column.

To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:

1. ₹ 50
2. ₹ 20
3. ₹ 40

The number of attempts made in three villages X, Y and Z are given below:

	(i)	(ii)	(iii)
X	400	300	100
Y	300	250	75
Z	500	400	150

Find the total cost incurred by the organisation for three villages separately, using matrices.

Construct a 2 × 3 matrix A = [a_ij] whose elements a_ij are give by:
a_ij = i.j