Solving 2 × 2 systems of equations, MATLAB in Engineering

Solving 2 × 2 systems of equations:

However this may be easy in a MATLAB, in normal finding solutions to the systems of equations is not. The systems which are 2 × 2 are, though, fairly clear-cut, and there are many methods of solution for such systems for which the MATLAB has built-in functions.

Consider the 2×2 system of equations which is as shown below:

1031_Solving 2 × 2 systems of equations.png

At first, to visualize the solution, it will be simpler to change both the equations to equation of a straight line by writing each in the form y = mx + b (by altering x1 to x and x2 to y):

2130_Solving 2 × 2 systems of equations1.png

In MATLAB we can plot these lines by using a script; the answers are shown in figure.

778_Solving 2 × 2 systems of equations2.png

2016_Solving 2 × 2 systems of equations3.png

The intersection of the lines is the point (4, -1). In another words, x = 4 and y = -1. Altering back to x1 and x2, we hold x1 = 4 and x2 = -1. This permits us to visualize the solution.

This system of equations in a matrix form is as shown below:

1793_Solving 2 × 2 systems of equations4.png

We know that the solution is x = A-1 b, therefore we solve this when we can find the inverse of A. The one technique of finding the inverse for a 2 × 2 matrix includes computing the determinant D.


´ For a 2× 2matrix A=

719_Solving 2 × 2 systems of equations5.png

The determinant D is defined as follows:


1027_Solving 2 × 2 systems of equations6.png

It is written by using vertical lines around the coefficients of the matrix, and is defined as the product of the values on the diagonal minus the product of the other two numbers.

For a 2 × 2 matrix, the matrix inverse is defined in terms of D as shown below:

1377_Solving 2 × 2 systems of equations7.png

Posted Date: 10/22/2012 3:07:57 AM | Location : United States

Related Discussions:- Solving 2 × 2 systems of equations, Assignment Help, Ask Question on Solving 2 × 2 systems of equations, Get Answer, Expert's Help, Solving 2 × 2 systems of equations Discussions

Write discussion on Solving 2 × 2 systems of equations
Your posts are moderated
Related Questions
Creating the structure Variables: Creating a structure variable can be accomplished by simply storing the values in fields by using assignment statements, or by using the stru

Appending variables to the Mat-File: Appending to the file adds to what has been saved in a file, and is accomplished by using the -append option. For illustration, supposing

I have a 400x2 vel.dat and 20x2 xy.dat file, how can i plot a streamslice graph on matlab with this two files.

Creating a cell array: The other method of creating a cell array is easy to assign values to particular array elements and build it up element by element. Though, as explained

Illustration of Vectors of structures: In this illustration, the packages are vector which has three elements. It is shown as a column vector. Each and every element is a stru

Finding a sting - function strfind: The function strfind does necessarily similar thing, except that the order of the arguments does make dissimilarity. The common form is str

function numden: The function numden will return individually the numerator & denominator of a symbolic expression: >> sym(1/3 + 1/2) ans = 5/6 >> [n, d] =

Data structures: The Data structures are variables which store more than one value. In order to made sense to store more than one value in a variable, the values must in some

Illustration of Sorting strings: To sort on the rows rather than second dimension should be specified. >> sort(words,2) ans = Hello Hdowy Hi Gbdeo

Function fieldnames - structure functions: The function fieldnames will return the names of the fields which are contained in the structure variable. >> pack_fields = fiel