Reference no: EM13124984
Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them.
1. Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints.
One typical application is to maximize profits. For example, a beauty parlor provides both highlighting and permanent wave services. It costs $5 in materials and requires 30 minutes to provide highlighting. However, it costs $12 in materials but requires 80 minutes to provide a perm. The store has at most $120 in materials and 800 minutes in labor per day to expend.
How many highlighting services and how many perms can the beauty parlor perform daily?
2. You are given the following system of linear equations:
3x - 2y + z = 2
-x + y = 3
-2y + 6 = -1
a. Provide a coefficient matrix corresponding to the system of linear equations.
b. What is the inverse of this matrix?
c. What is the transpose of this matrix?
d. Find the determinant for this matrix.
3. Calculate the following for
a. A * B
b. -3A
c. A-1
4. Solve the following linear system using Gaussian elimination.
Show work.
2y + z = 4
x+ y +z = 6
2x + y + z = 7
5. Solve the following linear system for x using Cramer's rule.
Show work.
4x - y + z = -5
2x + 2y + 3z = 10
5x - 2y + 6z = 1
Human populations can be modeled using an exponential growth function. Use the Library for research or other resources to find the following:
- current world population
- current U.S. population
- current growth rate of the world population
- current growth rate of the U.S. population
Starting in the current year, determine the following:
1. Based on current growth rates, how long will it take world population to reach exactly 7 billion? How long to reach exactly 10 billion?
2. Based on current growth rates, how long will it take for the U.S. population to reach exactly 300 million? How long for exactly 400 million?
|
Problem regarding property taxes
: On July 1, 2009, Cheryl pays the entire real estate tax of $5,475 for the year ending December 31, 2009. a. How much of the property taxes may Phil deduct?
|
|
Confidence intervals for variance and standard deviation
: Assume that the lives of all such bulb (approximately) normally distribution. Make the 99% confidence intervals for the variance and standard deviation of the lives of all such bulbs.
|
|
Solving systems of differential equations
: Step by step process in solving the following question. Using matrix algebra techniques, find a general solution of the system:
|
|
Can kristen deduct the dinners she purchased
: During the year, Krisiten holds two jobs. After an eight-hours day at the first job, she works three hours at the second job. On Fridays of each week, she returns home for dinner before going to the second job.
|
|
Solving systems of linear equations-matrix methods
: Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them.
|
|
Case involving a taxpayer
: The Federal Circuit Court has ruled that wholesale distribution and retail sales, even of the same product, constitutes distinct businesses. In a case involving a taxpayer from another circuit, the Tax Court has ruled that such costs invariably sh..
|
|
Solution of a strong acid
: Are the following statements about a 1.0 M solution of a strong acid, HA, true or false? [A-] › [H+]: True/False
|
|
Solving inequalities and linear systems of equations
: Find the solution to the following system of linear equations: Solve the following absolute value inequality: ½ |x - 2|
|
|
Inventories reflected by accounting records
: Carly Manufacturing Company's accounting records reflect the following inventories:
|