1 / 8

Understanding Matrix Multiplication: Dimensions and Possibilities

Explore the fundamentals of matrix multiplication in this concise guide. Learn about the importance of dimension compatibility, as the number of columns in the first matrix must equal the rows in the second. Discover how to determine the dimensions of the resulting product matrix based on the given matrices. This guide provides insight into whether specific multiplications are possible, and it details the process of multiplying matrices by summing the products of corresponding elements. Understand matrix multiplication’s rules and applications effectively.

nitsa
Download Presentation

Understanding Matrix Multiplication: Dimensions and Possibilities

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. Section 4.3 – Multiplying Matrices

  2. MATRIX MULTIPLICATION 1. The order makes a difference…AB is different from BA. 2. The number of columns in first matrix must equal number of rows in second matrix. In other words, the inner dimensions must be equal. 3. The answer will be number of rows in first matrix by number of columns in second matrix. In other words, the outside dimensions. Are the following matrix multiplications possible? 2 x 1 1 x 2 2 x 1 1 x 2

  3. YES NO YES YES 3 x 23 x 2 3 x 22 x 3 3 x 11 x 3 2 x 33 x 2 YES NO 2 x 22 x 2 3 x 3 2 x 2 Are the following matrix multiplications possible?

  4. YES YES NO YES 3 x 23 x 2 3 x 22 x 3 3 x 11 x 3 2 x 33 x 2 YES NO 2 x 22 x 2 3 x 3 2 x 2 What is the dimension of the following products, if possible? 2 x 2 3 x 3 3 x 3 2 x 2

  5. MATRIX MULTIPLICATION The product of two matrices is found by multiplying the corresponding elements in each row by each column and then adding them together. ROW…COLUMN

  6. MATRIX MULTIPLICATION SUMMARY 1. Is the multiplication possible? 2. If yes, what is the dimension of the product? 3. Create a “blank” matrix. 4. “Multiply/Add” corresponding rows and columns

More Related