{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MA 405 Final Examination Solutions

MA 405 Final Examination Solutions - Lin Alg Matrices Final...

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

View Full Document Right Arrow Icon
Lin Alg & Matrices Final Examination Spring 1996 Your Name: SOLUTION For purpose of anonymous grading, please do not write your name on the subsequent pages. This examination consists of 5 questions, each question counting for the given number of points, adding to a total of 24 points. Please write your answers in the spaces indicated, or below the questions (using the back of the sheets if necessary). You are allowed to consult two 8 . 5 0 × 11 0 sheets with notes, but not your book or your class notes. If you get stuck on a problem, it may be advisable to go to another problem and come back to that one later. You will have 2 hours to do this test. Good luck! Problem 1 2 3 4 5 Total 1
Image of page 1

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

View Full Document Right Arrow Icon
Problem 1 (7 points): Please answer the following questions and justify your answers briefly. (a, 2pts) Consider the following 2 problems: A. Given a basis for a subspace of R n find a basis for its orthogonal complement. B. Given a matrix and one of its eigenvalues, find a basis for the corresponding eigenspace. Both problems can be reduced to the problem of finding a basis for the nullspace of a matrix. Please explain what those nullspace problems look like. A. Let v 1 , . . . , v r be a basis for V R n . Write A = [ v 1 | v 2 | . . . | v r ]. Then V = CS ( A ), hence V = CS ( A ) = NS ( A T ). B. The eigenspace is NS ( A - λ 1 I ) where λ 1 is the eigenvalue. (b, 1pts) For the following weighted inner product on R 3 , h x , y i = x 1 y 1 + 2 x 2 y 2 + x 3 y 3
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the 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