Matrix solutions of the linear algebraic equation, MATLAB in Engineering

Matrix solutions to systems of the linear algebraic equations:

The linear algebraic equation is an equation of the form

a1x1 + a2x2 + a3x3   .  .  .  .  anxn = b

Where a's are the constant coefficients, the x's are the unknowns, and b be constant. A solution is a series of numbers s1, s2, and s3 which satisfy the equation. The illustration is as follows,

4x1 +  5x2 - 2x3 = 16

is such an equation in which there are 3 unknowns: x1, x2, and x3. The One solution to this equation is x1 = 3, x2 = 4, and x3 = 8, as 4 * 3 + 5 * 4 - 2 * 8 is equal to 16.

The system of linear algebraic equations is a set of equations of the form:

621_Matrix solutions of the linear algebraic equation.png

 

This is known as m × n system of equations; there are m equations and n unknowns.

As of the way that matrix multiplication works, such equations can be presented in matrix form as Ax = b here A is a matrix of the coefficients, x is the column vector of the unknowns, and b is the column vector of constants from the right-hand side of the equations:

A solution set is a set of all the possible solutions to the system of equations (all sets of values for the unknowns which solve the equations). All the systems of linear equations have either:

  •  No solutions
  •  One solution
  •  Infinitely many solutions

The one of the main concepts of the subject of linear algebra is the various techniques of solving (or trying to solve!) systems of the linear algebraic equations. The MATLAB has many functions which assist in this process.

The system of equations has been once written in matrix form, what we want is to evaluate the equation Ax = b for the unknown x. To do this, we require to isolate x on one side of the equation. If we were working with scalars, then we divide both sides of the equation by x. However, with the MATLAB we can use the divided into operator to do this. Though, most languages cannot do this with matrices, therefore we rather multiply both sides of the equation by the inverse of the coefficient matrix A:

A-1 A x = A-1 b

Then, as multiplying a matrix by its inverse results in the identity matrix I, and since multiplying any matrix by I answers in the original matrix, we contain:

I x = A-1 b

or

x = A-1 b

This means that the column vector of unknown x is found as the inverse of matrix A multiplied by the column vector b. Therefore, if we can find the inverse of A, we can resolve for the unknown in x.

Posted Date: 10/22/2012 2:45:36 AM | Location : United States







Related Discussions:- Matrix solutions of the linear algebraic equation, Assignment Help, Ask Question on Matrix solutions of the linear algebraic equation, Get Answer, Expert's Help, Matrix solutions of the linear algebraic equation Discussions

Write discussion on Matrix solutions of the linear algebraic equation
Your posts are moderated
Related Questions
Example Exit modular program: In the illustration below, the user  Chose the Limit; -   Whenever prompted for n, entered the two invalid values before finally ente

Finding sums and products: A very general application of a for loop is to compute sums and products. For illustration, rather than of just printing the integers 1 through 5, w

Patch function - graphics objects: The patch function is used to generate a patch graphics object, which is made from 2-dimensional polygons. The patch is defined by its verti

Intersect function and setdiff function: The intersect function rather than returns all the values which can be found in both of the input argument vectors. >> intersect(v

Binary Search: The binary search supposes that the vector has been sorted first. The algorithm is just similar to the way it works whenever looking for a name in a phone direc

deblank function: The deblank function eliminates only trailing blanks from the string, not leading the blanks. The strtrim function will eliminate both the leading and traili

Evaluating a string: The function eval is used to compute a string as a function. For illustration, below is the string 'plot(x)'is interpreted to be a call to plot the functi

Individual structure variable: The individual structure variable for one software package may look like this: The name of the structure variable is a package; it has f

readlenwid function: function call: [length, width] = readlenwid; function header: function [l,w] = readlenwid In the function call, not any argument is passed; henc

True color matrice: The true color matrices are the other way to represent images. The true color matrices are 3-dimensional matrices. The first two coordinates are the coordi