1 / 11

Fundamentals of Engineering Analysis

Cramer’s Rule for solving linear systems Part 1 . Fundamentals of Engineering Analysis . Eng. Hassan S. Migdadi. Coefficient Matrices. You can use determinants to solve a system of linear equations. You use the coefficient matrix of the linear system.

penny
Download Presentation

Fundamentals of Engineering Analysis

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. Cramer’s Rule for solving linear systems Part 1 Fundamentals of Engineering Analysis Eng. Hassan S. Migdadi

  2. Coefficient Matrices You can use determinants to solve a system of linear equations. You use the coefficient matrix of the linear system. Linear SystemCoeff Matrix ax+by=e cx+dy=f

  3. Cramer’s Rule for 2x2 System Let A be the coefficient matrix Linear SystemCoeff Matrix ax+by=e cx+dy=f If detA 0, then the system has exactly one solution: and

  4. Example 1- Cramer’s Rule 2x2 Solve the system: 8x+5y=2 2x-4y=-10 The coefficient matrix is: and So: and

  5. Solution: (-1,2)

  6. Example 2- Cramer’s Rule 2x2 Solve the system: 2x+y=1 3x-2y=-23 The solution is: (-3,7) !!!

  7. Example 3- Cramer’s Rule 3x3 Solve the system: x+3y-z=1 -2x-6y+z=-3 3x+5y-2z=4 Let’s solve for Z Z=1 The answer is: (-2,0,1)!!!

  8. Solving 3D Linear System using Cramer’s Rule

  9. Example: 2x + y + z = 3 x – y – z = 0 x + 2y + z = 0

  10. Determinants of XYZ =3 X= 1, y =-2, z=3 =3 =-6 =9

  11. Given the following system of equations, find the value ofz. 2x + y + z = 1 x – y + 4z = 0 x + 2y – 2z = 3 =-3 =-6 Z=2

More Related