# mockdex2 - Math 4377 Linear Algebra Mock Second Exam Summer...

This preview shows pages 1–3. Sign up to view the full content.

Math 4377, Linear Algebra, Mock Second Exam. Summer 2011, Dr. Min Ru, University of Houston This is a closed book and closed note test. You have two hours to do the test. It is a good idea to read the entire exam before answering any question, and to plan your time wisely. At the end of test, don’t forget to write your name on anything you submit. Good luck!!! Name (Printed): Student ID : Remark : Throughout the exam, P n ( R ) is the vector space of real poly- nomials of degree n . 1

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

View Full Document
1. Answer each of the following as true or false (state a brief reason). (a) If T : P 2 ( R ) P 1 ( R ) is the linear transformation defined by T ( ax 2 + bx + c ) = ( a - c ) x + ( b + c ), then x 2 + 2 x + 1 is in N ( T ), the null space of T . (b) If T : R 2 R 2 is the linear transformation defined by T ( x, y ) = ( x - y, x + y ). Then (2 , 3) R ( T ), the range of T . (c) Let T : R 2 R 2 be the transformation defined by T ( x, y ) = ( x 2 - y 2 , x 2 + y 2 ), then T is linear. (d) Let T : R 7 R 5 be a linear transformation. If nullity( T ) = 3, then rank( T ) = 2.
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