Stitz-Zeager_College_Algebra_e-book

As we will see in section 852 determinants specically

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: × n matrices, Im A = AIn = A. • Distributive Property of Matrix Multiplication over Matrix Addition: A(B ± C ) = AB ± AC and (A ± B )C = AC ± BC The one property in Theorem 8.5 which begs further investigation is, without doubt, the multiplicative identity. The entries in a matrix where i = j comprise what is called the main diagonal of the matrix. The identity matrix has 1’s along its main diagonal and 0’s everywhere else. A few examples of the matrix Ik mentioned in Theorem 8.5 are given below. The reader is encouraged to see how they match the definition of the identity matrix presented there. [1] I1 8 10 01 I2 1 100 0 0 1 0 0 001 0 I3 0 1 0 0 0 0 1 0 0 0 0 1 I4 And may not even have the same dimensions. For example, if A is a 2 × 3 matrix and B is a 3 × 2 matrix, then AB is defined and is a 2 × 2 matrix while BA is also defined... but is a 3 × 3 matrix! 484 Systems of Equations and Matrices The identity matrix is an example of what is called a square matrix as it has the same number of rows as...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online