on:—RS 121 is the cost of 5kg of sugar, 5kg of wheat and 2kg of rice. The cost of 4kg rice, 2kg sugar and 5kg wheat is Rs 89. The cost of 3kg wheat, 2kg rice and 4kg sugar is Rs 95. Find the cost of each PER kg by matrix method. *Answer:—→ Sugar = Rs 40, → Wheat = Rs 18 and → Rice = Rs 25Step-by-step explanation:—→ Let the cost of 1 kg of sugar be Rs x→ Let the cost of 1 kg of wheat be Rs y→ Let the cost of 1 kg of rice be Rs z∴Cost of 5 kg sugar, 5 kg wheat, 2 kg rice = Rs 340 Cost of 2 kg sugar, 5 kg wheat, 4 kg rice = Rs 270 Cost of 4 kg sugar, 3 kg wheat, 2 kg rice = Rs 264Required system of linear equations:—5x + 5y + 2z = 3402x + 5y + 4z = 2704x + 3y + 2z = 264 ∴ AX = BPre multiplying by A⁻¹,X = A⁻¹B _______________(1)For matrix A,|A| = 5(10-12) -5(4-16) +2(6-20)or |A| = 22Thus, A is invertibleFinding COFACTORS of matrix A→ C₁₁ = -2, C₁₂ = 12, C₁₃ = -14→ C₂₁ = -4, C₂₂ = 2, C₂₃ = 5→ C₃₁ = 10, C₃₂ = -16, C₃₃ = 15∴Cofactor matrix of A :—Therefore,→ A⁻¹ = 1/ |A| ( adj A)or,Substituting in EQUATION 1,or,or,or,Thus, → x=40, → y=18, → z=25So, According to this we get:—Cost of 1 kg of sugar is Rs 40Cost of 1 kg of wheat is Rs 18Cost of 1 kg of rice is Rs 25