Find x, if

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below:

(a) If unit sale prices of x, y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively, find the total revenue in each market with the help of matrix algebra.

(b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise respectively. Find the gross profit.

If then show that A is a root of the polynomial f(x) = x³ – 6x² + 7x + 2.

Find the inverse of each of the following matrices by using elementary row transformations:

Let, show that (aI + bA)ⁿ = aⁿI + na^n-1bA, where I is the identity matrix of order 2 and n ϵ N.