Matrix solutions of the linear algebraic equation, MATLAB in Engineering

Assignment Help:

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.


Related Discussions:- Matrix solutions of the linear algebraic equation

Distributed computing on linux cluster, i want to run 4 instances of my mat...

i want to run 4 instances of my matlab code on 4 processor cores. im executing the job from head node. i created a parallel job and assigned number of workers. but i don''t get bac

Signals, Q.1: Consider the transmission of a sinusoid x(t) = cos(2f0t) thr...

Q.1: Consider the transmission of a sinusoid x(t) = cos(2f0t) through a channel a ected by multipath and Doppler. Let there be two paths, and assume the sinusoid is being sent fro

Displaying expressions, Displaying expressions: The good-looking funct...

Displaying expressions: The good-looking function will show such expressions by using exponents; for illustration, >> b = sym('x^2') b = x^2 >> pretty(b)

Sound files, Sound Files: The sound signal is an illustration of a con...

Sound Files: The sound signal is an illustration of a continuous signal which is sampled to result in a discrete signal. In this situation, sound waves traveling through the a

Program to examine exponential function, Write a program to examine exponen...

Write a program to examine exponential function: We will write a program to examine the value of e and the exponential function. It will be a menu-driven. The menu options wil

Str2num function - string, str2num function - String: The function str2...

str2num function - String: The function str2num does the opposite; it takes the string in which a number is stored and converts it to the type double: >> num = str2num('123.

Variable scope, Variable Scope: The scope of any of variable is the wo...

Variable Scope: The scope of any of variable is the workspace in which it is valid. The workspace generated in the Command Window is known as the base workspace. As we know

Execution steps - modular program, Execution steps: Whenever the progr...

Execution steps: Whenever the program is executed, the steps below will take place: The script calcandprintarea starts executing. The calcandprintarea calls the readr

Square matrices, Square Matrices: If a matrix has similar number of ro...

Square Matrices: If a matrix has similar number of rows and columns, for illustration, if m == n, the matrix is square matrix. The definitions which follow in this part apply

Structures, Structures: The Structures are data structures which group...

Structures: The Structures are data structures which group together values which are logically related in what are known as the fields of structure. The benefit of structures

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd