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.
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
Let's assume that we have to solve the following problem:
The question is: what is the cost of each apple, pear and cucumber?
We can describe the problem by:
- 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
or, using x1 for apple, x2 for pear und x3 for cucumber:
- 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
- 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:
The augmented matrix is then:
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.
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.