Operation on Matrices.pptx

Uploaded by Tshering Tashi of Sonamthang Central Schol, Panbang: Zhemgang, 2022

1. Operation on Matrices Addition, subtraction and multiplication  are the basic operations on the matrix. Addition & subtraction: Two matrices must have same order and add or subtract their corresponding or matching elements. Example: If , Then +  

2. The sum/differences ( of two matrices of the same order, and , is the matrix in which the entry of in the and is , for Thus if and , For Example: Consider, Dorji and Nado are close competitors in a class ten in 2021 in math and science. They compare their marks at the end of the academic year. Find their sum and differences of their scores in two subjects.   Mid-term Examination, 2021 Subject & Name Dorji Nado Math 95 90 Science 85 87 Annual Examination, 2021 Subject & Name Dorji Nado Math 90 92 Science 88 89

3. Student Activity. Is it possible to define the matrix , when A has 3 rows and B has 2 rows A has 3 columns and B has 2 columns A has 3 rows and B has 2 columns Both A and B are square matrices of the same order. Solution:  

4. Negative of the Matrix The negative of the matrix denoted by is the matrix formed by replacing each entry in the matrix with the additive inverse. For Example, If , then and is any matrix of the same order such that , the zero matrix, then is called the additive inverse of A. That is Find the additive inverse of ?  

5. Theorem: If , where are any given natural numbers and  

6. Let A , B , and C be m x n matrices and let c and d be scalars.

7. Example: Solving a Matrix Equation Solve the matrix equation: 2 X – A = B for the unknown matrix X , where: We use the properties of matrices to solve for X . 2 X – A = B 2 X = B + A X = ½( B + A )