# C3091424 - 24(Statement of the problem Proof a Since A is...

• Notes
• 1

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

24. (Statement of the problem.) Proof. a) Since A is row equivalent to B , by the definition, there are elementary matrices E 1 , · · · , E k such that A = E k · · · E 1 B. (1) Since B is row equivalent to C , by the definition, there are elementary matrices F 1 , · · · , F j ( Note: Use different notation! ) such that B = F j · · · F 1 C. (2) Substitute (2) into (1) we get A = E k · · · E 1 F j · · · F 1 C. Since E 1 , · · · , E k , F 1 , · · · , F j are elementary matrices, by the definition, A is row equivalent to C . b) Suppose both A and B are nonsinngular n × n matrices. By Theorem 1.4.2, A is row equivalent to I and B is row equivalent to I . Since
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: I , by Problem 23, I is row equivalent to B . So we have that A is row equivalent to I and I is row equivalent to B . By Part (a), we get that A is row equivalent to B . / ——————– A short version of Part (b) is like the following: Suppose both A and B are nonsinngular n × n matrices. By Theorem 1.4.2, A is row equivalent to I and B is row equivalent to I . By Problem 23, I is row equivalent to B . By Part (a), A is row equivalent to B . / 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern