# How to solve linear equation system

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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.

Copy the questions to a Microsoft Word document and use an equation editor to enter the answers. Please answer the following questions about matrices.

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?

You are given the following system of linear equations:

3x - 2y + z = 2

-x + y = 3

-2y + 6 = -1

Provide a coefficient matrix corresponding to the system of linear equations.

What is the inverse of this matrix?

What is the transpose of this matrix?

Find the determinant for this matrix.

Calculate the following for

A * B

-3A

A-1

Solve the following linear system using Cramer's rule.n.

Show work.

2y + z = 4

x+ y +z = 6

2x + y + z = 7

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

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##### Solution Summary

The solution contains detailed explanation of solving linear equation systems by Gaussian elimination method or Cramer's rule; and solving linear programming problems.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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