© 2005 Baylor University Slide 1 Fundamentals of Engineering Analysis EGR 1302 Unit 1, Lecture C Approximate Running Time - 14 minutes Distance Learning / Online Instructional Presentation Presented by Department of Mechanical Engineering Baylor University Procedures: 1.Select “Slide Show” with the menu: Slide Show|View Show (F5 key), and hit “Enter” 2.You will hear “CHIMES” at the completion of the audio portion of each slide; hit the “Enter” key, or the “Page Down” key, or “Left Click” 3.You may exit the slide show at any time with the “Esc” key; and you may select and replay any slide, by navigating with the “Page Up/Down” keys, and then hitting “Shift+F5”.

© 2005 Baylor University Slide 2 Solving Systems of Linear Equations The Inverse Matrix A nxn and B nxn are Square Matrices of the same Order. A * B = I n B * A = I n B is called “The Inverse of A” B = A -1 A * A -1 = I in Algebra, the equivalent is

© 2005 Baylor University Slide 3 Solving Systems of Linear Equations Sum of Products The same equation can represent any Order.

© 2005 Baylor University Slide 4 ( ) Solving this System for x 1, x 2 Becomes Subtract

© 2005 Baylor University Slide 5 Solving this System for x 1, x 2 (cont.) Sum of Products A new Matrix “C” factor out the denominator

© 2005 Baylor University Slide 6 We now have a solution for the Inverse of a 2x2 Matrix The Solution to

© 2005 Baylor University Slide 7 The Determinant The Determinant of A =

© 2005 Baylor University Slide 8 Rules for Finding the Inverse of a 2x2 Matrix Rule 1: Swap the Main Diagonal Rule 2: Change Signs on the Back Diagonal Rule 3: Divide by the Determinant

© 2005 Baylor University Slide 9 Review of the Solution to a 2x2 System Is solved by If there is no solution Stay Tuned!

© 2005 Baylor University Slide 10 A Numerical Example Becomes

© 2005 Baylor University Slide 11 This concludes Unit 1, Lecture C