# Solving linear equation systems

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.

https://brainmass.com/math/linear-algebra/130610

#### Solution Summary

The solution contains detailed explanation of how to solve the linear equation system by using matrix method or Gaussian elimination.