Three persons A, B and C possess Tk.3000, Tk.2000 and Tk.2500 respectively. A with his entire amount purchased 5 shares of Tk. X each, 3 shares of Tk. Y each and 4 shares of Tk. Z each. B purchased 3 shares of Tk. X each, 4 shares of Tk. Y each and 2 shares of Tk. Z each with his entire amount and C purchased 4 shares of Tk. X each, 3 shares of Tk. Y each and 4 shares of Tk. Z each with his entire amount. a. What is Cramer's rule? b. When Cramer's rule does not applicable? c. Write down the system of linear equation (SLE) using the above information. d. Write down the coefficient matrix and the column vector of constants from (c). e. Figure out the value of determinant of the corresponding coefficient matrix from the above SLE using Laplace method. f. Determine the value of each share of different types. 20 2. A manufacturer produces three products P, Q and R, which he sells in two markets. Annual sales volumes are indicated as follows: P Q R Markets: 2 1 6000 20000 8000 10000 2000 18000 If the unit sales price of P , Q and R are Tk. 2.50, Tk. 1.25, and Tk. 1.50 respectively and if the unit costs of the above three commodities are Tk. 1.80, Tk. 1.20 and Tk. 0.80 respectively. (a) Write down the condition of matrix multiplication and matrix addition. (b) Express the unit sales prices and unit cost prices as a three element column matrix and write down their dimension. (c) Find the total revenue in each markets with the help of matrix algebra. (d) Find the total cost in each market. (e) Find the profit in each market. (f) Find the gross profit of the manufacturer company from the market 1 and 2.