Math 141 – Summer 2014 Additional Problems – Matrices, Linear Models Additional Problems 1. Which of the following is true for the system of equations x – 3y + 2z = 4 y + 2z = – 3 x +4z – 7u = 10 2z + 10u = 20 a) Unique solution with ( x, y, z, u ) = (– 24.13, – 3.43, 8.91, 0.22) b) Unique solution with ( x, y, z, u ) = (84.23, 19.31, -11.15, 4.23) c) Infinitely many solutions d) No solution 2. Solve the system of equations. If there are infinitely many solutions, then write the parametric solution. x+ 2y + 6z = 8 x + y + 3z = 4 3. Nina has some quarters, pennies and dimes. The total face value of the coins is $6.48. The number of dimes is 6 more than twice the total number of pennies and quarters. If there are a total of 66 coins, find the number of quarters, pennies and dimes that Nina has. 4. Matrix A represents the type of furniture item – chair, footstool, couch, and the units of Wood, Fabric and Stuffing required for each piece of furniture. Wood costs $15 per unit, Fabric costs $25 per unit, and Stuffing costs $7 per unit. Wood 2 Fabric 2 Stuffing 1 3 1 1 Footstool 1 3 3 Couch Chair A= a) Write the column matrix B that represents the per unit cost of Wood, Fabric, and Stuffing. Clearly label what the rows and columns of B represent. b) Find the product AB. State, in words, what product represents. c) What is the total cost of making 3 chairs, 3 footstools, and 3 couches? Math 141 – Summer 2014 Additional Problems – Matrices, Linear Models 5. Find a, b, c, given that a+b 2c – b 2b + 3d + c 4a – 3d 3 –1 1 0 2 5 –4 5 + 6. Given 2x + 3y = 6. If x increases by 10, what is the corresponding change in y ? 7.Find the equation of a vertical line that passes through the point (1,4). 8. Find the equation of the horizontal line passing through (2,-3). 9.It costs a company $2000 to produce 1000 markers per month and $1200 if they don't produce anything. If they sell the markers for $0.90 each, and the cost, revenue and profit functions are known to be linear, determine how many markers should they make in a month to break even. 10. For a price of $300, the quantity demanded of a certain brand of media player is 2000 per month. For each decrease in the unit price of $40 below $300, the quantity demanded increases by 160 units. The suppliers will not market any music players if the unit price is $200 or lower. But they will make 1800 units available at a unit price of $500. The demand and supply equations are known to be linear. Find the equilibrium price, p, and quantity, x.