Math Exam Final Review Worksheet With Answer Key - M118, Indiana University Southeast Page 3
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1229) Solve by augmented matrix methods using Gauss-Jordan elimination: Show your initital matrix and final
solution.
x 1 - 3x 2 - 5x 3 = -30
x 2 - 3x 3 = 12
x 1
+ x 3 = -9
2 -3 4
5
3 -3
30) Find
3
-
0 -1 1
1 -6 2
7 0 2
-1 4 8
5 -2
31) Given A = 2 -3 1
and
B =
,
0 3
6 -1 0
-6 1
find AB and BA and label your results.
8 -4 a
32) Find the inverse of
0 1 0
1 0 1
and tell under which conditions the inverse does not exist.
33) Solve by augmented matrix methods using Gauss-Jordan elimination: Show your initial matrix and final
solution.
2x 1 + 2x 2 = -10
2x 1 - 4x 2 = 8
x 1 + x 2 = -5
34) A performance center has 2,500 seats. Tickets for an event are $6 and $8 per seat. Assuming that all ticketes
are sold and bring in a total of $17,200, how many of each type of ticket were sold? Set up a system of
equations and solve by augmented matrix methods using Gauss-Jordan elimination.
35) If $9,000 is to be invested, part at 13% and the rest at 8%, how much should be invested at each rate so that the
total annual return will be the same as $9,000 invested at 9%? Set up a system of equations, letting x 1 be the
amount invested at 13% and x 2 be the amount invested at 8%.
36) In producing three types of bricks: face bricks, common bricks, and refractory bricks, a factory incurs labor,
material, and utility costs. To produce one pallet of face bricks, the labor, material, and utility costs are $50,
$75, and $35, respectively. To produce one pallet of common bricks, the labor, material, and utility costs are
$50, $60, and $30, respectively, while the corresponding costs for refractory bricks are $75, $100, and $45. In a
certain month the company has allocated $12,000 for labor costs, $14,500 for material costs and $6,000 for
utility costs. How many pallets of each type of brick should be produced in that month to exactly utilize these
allocations? Set up a system of linear equations, letting x, y, and z be the number of pallets of face, common,
and refractory bricks, respectively, that must be produced in that month.
37) A hospital dietitian wants to ensure that a certain meal consisting of rice, broccoli, and fish contains exactly
26,800 units of vitamin A, 840 units of vitamin E, and 11,160 units of vitamin C. One ounce of rice contains
400 units of vitamin A, 20 units of vitamin E, and 180 units of vitamin C. One ounce of broccoli contains 800
units of vitamin A, 60 units of vitamin E, and 540 units of vitamin C. One ounce of fish contains 2,400 units of
vitamin A, 40 units of vitamin E, and 810 units of vitamin C. How many ounces of each food should this meal
include? Set up a system of linear equations and solve using Gauss-Jordan elimination.
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