{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

04win-f

# 04win-f - MATH 51 FINAL EXAM Professors Clingher Munson and...

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

MATH 51 FINAL EXAM Professors Clingher, Munson, and White March 15, 2004 1 Consider the matrices A = 1 1 0 0 2 2 2 0 1 6 0 1 - 1 1 3 - 1 - 2 1 1 - 1 and R = 1 0 1 0 1 0 1 - 1 0 1 0 0 0 1 2 0 0 0 0 0 . The matrix R is the row reduced echelon form of A . (You do not need to check this.) 1(a). Find a basis for the column space of A . 1(b). Find a basis for the column space of R . 1(c). Find a basis for the nullspace of A . 2. Find all solutions of x 1 + 2 x 2 + x 3 + x 4 = 7 x 1 + 2 x 2 + 2 x 3 - x 4 = 12 2 x 1 + 4 x 2 + 6 x 4 = 4 . 3(a). Find all eigenvalues of the matrix A = 5 0 0 1 2 1 1 1 2 . 3(b). The matrix M = 5 - 6 - 6 - 1 4 2 3 - 6 - 4 has λ = 2 as one of its eigenvalues. (You need not check this.) Let V be the eigenspace corresponding to this eigenvalue. (In other words, V consists of all eigenvectors with eigenvalue 2 together with the origin.) Find a basis for V . 4. The velocity of a certain spaceship at time t is given by v ( t ) = (3 t 2 , e t - 1 , 6 t ). At time t = 1, its position is (0 , 0 , 7). (a) Find the speed at time t .

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.

{[ 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