1 / 8

Guass-jordan Reduction :

Guass-jordan Reduction :. Step 1 : Form the augmented matrix corresponding to the system of linear equations. Step 2 : Transform the augmented matrix to the matrix in reduced row echelon form by using elementary row operations.

skylar
Download Presentation

Guass-jordan Reduction :

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Guass-jordan Reduction : Step 1: Form the augmented matrix corresponding to the system of linear equations. Step 2 : Transform the augmented matrix to the matrix in reduced row echelon form by using elementary row operations. Step 3 : Solve the linear system corresponding to the matrix in reduced row echelon form.

  2. Number of Solutions of a System of Linear Equations: • For any system of linear equations, precisely one of the following is true. • The system has exactly one solution. • The system has an infinite number of solutions. • The system has no solution.

  3. Exercise : 2.3 Page # 113Qn # 5 (b) Find all solutions, if any exist, by using the Gauss Jordan reduction method. Step 1 : Augmented matrix for the set is:

  4. Step 2 : The matrix in reduced row echelon form is Step 3 : The Solution is The given system has exactly one solution.

  5. Exercise 2.2, Page #114,Qn #7(c) • Solve the linear system, with given augmented matrix, if it is consistent. • Step 1 : • Step 2 : The matrix in reduced row echelon form is

  6. Step 3 : The linear system corresponding to the matrix in reduced row echelon form is • The solution are The given system has infinitely many solutions.

  7. Example • Solve for the following system • Step 1 : The augmented matrix is

  8. Step 3 : The matrix in reduced row echelon form is • Step 3 : The linear system corresponding to the matrix in reduced row echelon form is since , there is no solution.

More Related