# com01fA - DOCTORAL QUALIFYING EXAMlNATION FALL 2001...

This preview shows pages 1–7. Sign up to view the full content.

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

View Full Document

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

View Full Document

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.

Unformatted text preview: DOCTORAL QUALIFYING EXAMlNATION FALL 2001 Advanced Calculus & Linear Algebra NAME: IDﬁ: Start your answer on each question sheet. Attach all extra sheets you use to the appropriate sheet. Hand in all question sheets. Date: AUGUST 2?, 2001 Time of Exam: l—BPM Place of Exam: Stony Brook Union, Room 231 ID#: 1. Evaluate I : f01 d2: file-army. ED#: {JIM 2- LOT, In 2 0. 371:1: In 2 (311—1 + Ian—‘2) (1’1 2 2135 ' ‘ ‘ ) Find linlnamxn' 1D#: 3. Find the absolute maximum and minimum values of f(1:,y) : 11:2 + 12333,; + 2y2 deﬁned on the domain {(27, y) : 43.:2 + y"2 g 25}. _ 4. 1‘ Find the determinant of \ 1 1 ID#: ID#: 5. Suppose A is an rr—th order anti-symmetric matrix, Le. AT : ﬂ-A. Len D = diagw; d2 - - - of } be a diagonal mamx whose entries dhdg, - - - ,dn are greater than zero. Prove det(D + A) > 0' n 1D#: \ a b , ., ﬂ. . . . ) be a mamx over real ﬁeld H. bind necessary and sufﬁment COﬂdltIOﬂS 0n 6. LetA:(C d a. b, c, and d 50 that A is diagonalizable. ...
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