Take Home Quiz 1 Math 166 Print Name____________________

1. Write the system of equations in an augmented matrix. Reduce the matrix completely showing all row operations as instructed in class. Use the calculator rref to check your answer. Copy carefully or your problem might become more difficult. This is the only time you will have to reduce a 3x3 system.

2x + 6y + 4z = -224

-5x + 3y - z = 20

4x + y + z = 44

2. Each matrix represents the row reduced form of an augmented matrix for a system of equations in x, y, and z.

Write the complete solution set or state there is no solution. If the solution is infinite, give two particular solutions.

a)

b)

c)

d)

3. a) Show all work. Find AB and BA. Are they equal?

b) Find .

4. A candy company makes turtles, chocolate covered pecans and chocolate caramels. Their costs per pound for chocolate, caramel and pecans are $3, $1.50 and $2 respectively. Each pound of turtles uses 0.2 pound of chocolate, 0.3 pound of caramel and 0.5 pound of pecans. Each pound of chocolate covered pecans uses 0.2 pound of chocolate, no caramel and 0.7 pound of pecans. Each pound of chocolate caramels uses 0.4 pound of chocolate, 0.5 pound of caramel and no pecans. How much will it cost them to make 5 pounds of turtles, 6 pounds of chocolate covered pecans and 3 pounds of chocolate caramels. You must set up the information in three matrices and show a matrix product in the proper order which gives their total cost.