com01fA - DOCTORAL QUALIFYING EXAMlNATION FALL 2001...

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

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7
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

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern