© 2005 Baylor University Slide 1 Fundamentals of Engineering Analysis EGR 1302 Unit 1, Lecture E Approximate Running Time - 7 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 The Adjoint Matrix and the Inverse Matrix Recall the Rules for the Inverse of a 2x2: 1.Swap Main Diagonal 2.Change sign of a 12, a 21 3.Divide by determinant If the Cofactor Matrix is “transposed”, we get the same matrix as the Inverse And we define the “Adjoint” as the “Transposed Matrix of Cofactors”. And we see that the Inverse is defined as

© 2005 Baylor University Slide 3 Calculating the Adjoint Matrix and A detA Problem 7.13 in the Text adjA =

© 2005 Baylor University Slide 4 Complexity of Large Matrices Consider the 5x5 matrix, S To find the Adjoint of S (in order to find the inverse), would require Finding the determinants of 25 4x4s, which means Finding the determinants of 25*16 = 400 3x3s, which means Finding the determinants of 400*9 = x2s. (Wow!) Which is why we use computers (and explains why so many problems could not be solved before the advent of computers).

© 2005 Baylor University Slide 5 Class Exercise: Find the Adjoint of A Work this out yourself before going to the solution on the next slide

© 2005 Baylor University Slide 6 Class Exercise: Solution Notice that: detA = 0, therefore matrix A is singular. However, even though the Determinant is zero, the Adjoint still exists. This means that the Inverse does not exist.

© 2005 Baylor University Slide 7 This concludes Unit 1, Lecture E