FinalSample

# FinalSample - C A where A = 1 1 1 1 1-1 1-1 1-1(b Find the...

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

APAM-Linear Algebra: Final exam sample 2009

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

View Full Document
1. (a) For the following 3 x 3 matrix A , compute its determinant by using the cofactor formula and expanding along the third column. Show the values of the 3 cofactors you compute. A = 1 2 3 - 1 2 - 2 1 - 4 1 . (b) Consider the matrix B obtained from A by adding rows 1 and 3 to row 2. Should det( B ) equal det( A )? Why? 2. Give all values of x for which A has an eigenvalue equal to 2. A = 3 2 - 1 2 x 2 x - 2 3 . 3. (a) Use the Gram-Schmidt procedure to find an orthonormal basis of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: C ( A ) where: A = 1 1 1 1 1-1 1-1 1-1 . (b) Find the projection matrix P for projecting onto C ( A ) . Recall that with the factorization A = QR , the projection matrix P = A ( A T A ) ?1 A T becomes QQ T . (c) Check your answer for P by computing Pa 1 where a 1 is the ﬁrst column of A . 1...
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