08bAss4

# 08bAss4 - AS4/MATH1111/YKL/08-09 THE UNIVERSITY OF HONG...

This preview shows pages 1–2. Sign up to view the full content.

AS4/MATH1111/YKL/08-09 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1111: Linear Algebra Assignment 4 Due date : Apr 16, 2008 before 6:30 p.m. Where to hand-in : Assignment Box outside the lifts on the 4th floor of Run Run Shaw Remember to write down your Name , Uni. no. and Tutorial Group number . If you find difficulties, you are welcome to see the instructor, tutors or seek help from the help room. See “Information” at for availabilities. Normally we do not count assignment grades in your final score. Nevertheless, any discovered plagiarism will be referred to University Disciplinary Committee. 1. Let A R m × n and B R n × r be two matrices. (a) Show that the nullity of AB is greater than or equal to the nullity of B . (b) Show that if rank( A ) = n , then rank( B ) = rank( AB ). 2. (a) Let A = 1 1 2 0 1 1 1 3 4 . Show that R 3 = N ( A ) c ( A ), where N ( A ) is the nullspace and c ( A ) is the column space of A . Is it always true that R 3 = N ( B ) + c ( B ) for any 3 × 3 matrix B ?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the 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