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.