logging in or signing up Determinants and Inverses bsndev Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 252 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: September 18, 2009 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... By: anksrok (25 month(s) ago) niceeeeeeeeeeee Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript Determinants and Inverses : Determinants and Inverses How do you calculate determinants and inverses of 2 x 2 and 3 x 3 matrices? Slide 2: A multiplicative identity matrix is an n x n matrix with 1s along the main diagonal and 0s elsewhere. 2 x 2 Multiplicative Identity 3 x 3 Multiplicative Identity Slide 3: Remember from a previous lesson: If ab = 1, then b is the multiplicative inverse of a so… If A and X are square matrices and AX = XA = I, where I is the identity matrix, then X is the multiplicative inverse of A–written A-1. Slide 4: To show that 2 matrices are inverses of each other, show AB = I or BA = I. For example, show that B is the multiplicative inverse of A: Show that AB = I. Slide 5: Every square matrix with real number elements has a real number determinant. Determinants help you find inverses. To find the determinant of a 2 x 2 matrix, use the following formula: Notice: The brackets change to lines to represent Determinants. Slide 6: For example: 6(-3) – 2(-1) =-18 + 2 =-16 6(2) – 1(-3) =12 + 3 =15 a(a) – 3(2) =a2 - 6 Slide 7: To find the determinants of a 3 x 3 matrix, you will first need to recopy the first two columns. 1. Multiply the downward diagonals. 2. Multiply the upward diagonals. 3. Add the results. 4. Subtract the top sum from the bottom sum. Slide 8: Find the determinant of the matrix below: 1. Multiply the upward diagonals. We get 2, 0, 0. 2. Multiply the downward diagonals. We get 6, -12, and 0. 3. Find the sums. Sum = 2 Sum = -6 4. Subtract the top sum from the bottom sum. Det = -6 – 2 = -8!! Slide 9: Another example: Find the determinant of Recopy the first 2 columns. Multiply the upward diagonals. Multiply the downward diagonals. Find the sums. Subtract the sums. We get -9, 16, and 0. We get 2, -6, and 0. Sum = 7 Sum = -8 Determinant = -8 – 7 = -15!! You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.