Question

Solve the following system of equations, using matrices : 2/x + 3/y + 10/z = 4, 4/x – 6/y + 5/z = 1, 6/x + 9/y – 20/z = 2 where x, y, z ≠ 0

If A = [1 cot x; –cot x 1], show that A′A⁻¹ = [–cos 2x –sin 2x; sin 2x –cos 2x].

A scholarship is a sum of money provided to a student to help him or her pay for education. Some students are granted scholarships based on their academic achievements, while others are rewarded based on their financial needs. Every year a school offers scholarships to girl children and meritorious achievers based on certain criteria. In the session 2022 – 23, the school offered monthly scholarship of ₹ 3,000 each to some girl students and ₹ 4,000 each to meritorious achievers in academics as well as sports. In all, 50 students were given the scholarships and monthly expenditure incurred by the school on scholarships was ₹ 1,80,000. Based on the above information, answer the following questions :

If A = [1 2 −3; 2 0 −3; 1 2 0], then find A⁻¹ and hence solve the following system of equations : x + 2y − 3z = 1 2x − 3z = 2 x + 2y = 3