Finite Math
2.2-2.6 Review
Name _____________________________
Date ________________ Block ________
Solve the following systems by the Gauss-Jordan method.
1.
x + 8y = 13
-5x + 2y = 19
2.
2x + 4y + 2z = 6
2x + y + z = 16
x + y + 2z = 9
3.
x1 – x2 + x3 = 3
-2x1 + 3x2 + x3 = -8
4x1 – 2x2 + 10x3 = 10
(you will get a no solution)
4.
2x1 – 4x2 + 12x3 = 20
(You will get infinitely many…show as parametric solution)
-x1 + 3x2 + 5x3 = 15
3x1 – 7x2 + 7x3 = 5
5. Jenn and Christina were assigned to buy refreshments for the Math Club meeting.
They bought all the same items. Jenn bought 3 six-packs of drinks, 2 bags of chips, and 4
packages of cookies for a total cost of $22. Christina bought 2 six-packs of drinks, 4 bags
of chips, and 5 packages of cookies for a total cost of $26.30. After the meeting, Beth
agreed to buy the unused items at the purchase cost. She got 1 six-pack of drinks, 2 bags
of chips, and 4 packages of cookies for a total cost of $17.20. Find the cost of each item.
(Keep as decimals, not fractions) Solve by Gauss Jordan and then check your answer by using
inverse matrices on your graphing calculator.
Define the variables:
x=
y=
z=
Write three equations from the given
information.
6. Find the inverse of the following matrix:
2
1
3
4
by two methods:
Method 1: Through Gauss Jordan:
Method 2: Use the formula
7. Solve the following system by using inverse matrices.
No Calculator
a.
Set up first in AX = B form
b.
Find A-1
x + 3y = 5
2x + y = 10
c. Solve : X = A-1B
8. Solve the following system in matrix form AX = B, compute A-1 and use it to solve the
linear system. (use calculator)
x– y
=1
x + y + 2z = 2
x + 2y + z = 0
A-1 =
AX = B:
X=
#6 and 7 Set up equations and solve by inverse matrices on Graphing Calculator
6. Bill and Bob’s Hamburgers had a three-day special on hamburgers, french fries, and
small drinks. The owners asked that a record of sales be kept. After the sale ended, the
manager submitted the following report:
Day 1
Day 2
Day 3
Hamburgers
460
510
380
Fries
350
550
315
Drinks
390
495
355
Sales
$2055.50
$2532.75
$1760.25
Bill and Bob were pleased with the results of the special sale. Lindsay, the office
assistant, noticed the prices of the items were not given. Bill challenged her to determine
the prices. Assume you are Lindsay and find the prices of the three items.
Define variables, show AX = B and label.
7. A study showed that for young women a breakfast containing approximately ½ cup
OJ, 1 egg, 2 slices of bread, and 1 cup of milk will prevent a hungry feeling before
lunch.. The following table shows the content of four breakfast foods. How many
grams of protein, carbs, fat, and calories are necessary to make up the desired amount
of each food?
Protein
Carbs
Fat
Calories
1c
orange
juice
1
scrambled
egg
1 slice
of
bread
1 c milk
2
8
2
10
24
4
10
13
0
8
6
0
110
120
100
85