   Chapter 10.2, Problem 14ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 14-18, assume the entries of all matrices are real numbers.Prove that if I is the m × m identify matrix and A is any m × n matrix, then IA = A.

To determine

Prove that if I Is the m × m identify matrix and A Is any m x n matrix, then IA = A.

Assume the entries of all matrices are real numbers.

Explanation

Given information: I Is the m x m identify matrix and A Is any m x n matrix.

Proof:

Given: I Is the m x m identify matrix and A Is the m x n matrix

To prove: IA = A

PROOF:

By definition of a m × m identity-matrix:

I = (δij) with δij={1     if i=j0    if ij for all i,j=1,2,...,m

(IA)ij=ijth entry of IA          =r=1nδ ira rj          =δi1a1j+δi2a2j+

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