MasterAllRound: the PC calculator

Linear equation system solver

Solving a system of linear equations means finding those values for the unknowns of the system which satisfy all equations simultaneously. MasterAllRound solves quadratic, linear and single solution equation systems. There is no size restriction for MasterAllRound.

Cell editing

As with the matrix modules you have several options to edit the cells:

You can enter numbers. For example "2.55"
You can enter formulas. For example "1.5 * (5/7 + 3/8)^2"
You can work with number symbols

Example

Let's assume that we have to solve the following problem:

Mr. Smith buys 5 apples, 5 pears and 4 cucumbers. He pays 3.30 EUR
Ms. Miller buys 2 apples, 3 pears and 4 cucumbers. She pays 2.10 EUR
Mrs. Taylor buys 1 apples, 1 pears and 1 cucumbers. She pays 0.70 EUR

The question is: what is the cost of each apple, pear and cucumber? We can describe the problem by:

5 apples + 5 pears + 4 cucumbers = 3.30 EUR
2 apples + 3 pears + 4 cucumbers = 2.10 EUR
1 apples + 1 pears + 1 cucumbers = 0.70 EUR

or, using x₁ for apple, x₂ for pear und x₃ for cucumber:

5 x₁ + 5 x₂ + 4 x₃ = 3.30
2 x₁ + 3 x₂ + 4 x₃ = 2.10
1 x₁ + 1 x₂ + 1 x₃ = 0.70

In matrix formulation the problem is written as:
Lin. Gleichungssystem or respectively.

The augmented matrix is then: Lin. Gleichungssystem

The calculation with MasterAllRound is easy and straightforward:

Enter the number of equations, in our examples "3"
Enter the augmented matrix, i. e. the coefficients of the matrix and the column vector
Click on the "Run!" button

The result window pops up:

You would obtain the result: x₁ = 0.2; x₂ = 0.3; x₃ = 0.2.
That is: 1 apple costs 0.20 EUR, 1 pear costs 0.30 EUR and 1 cucumber costs 0.20 EUR.

Application examples

With MAR Plus you can easily and quickly obtain results for linear equation systems. Linear equation systems are commonly used in many professional areas. Here's an example of how to use a gozintograph in material management and the solution of the resulting linear equation system with MAR Plus.

Example - material management - gozintograph (pdf-file)