{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# quiz3 - 4 Find the inverse of the following n × n matrix A...

This preview shows page 1. Sign up to view the full content.

Math 54 Wednesday, February 11 Quiz 3 1. Suppose T and U are linear transformations from R n to R n such that T ( U ( x )) = x for all x R n . Is that true that U ( T ( x )) = x for all x R n . Explain. 2. What is the rank of a 4 × 5 matrix whose null space is three-dimensional? 3. Let A be a matrix and B be an echelon form of A : A = - 3 9 - 2 - 7 2 - 6 4 8 3 - 9 - 2 2 1 - 3 6 9 0 0 4 5 0 0 0 0 (a) Find a basis for Col A . (b) Find a basis for Nul A . 4. Find the inverse of the following
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . 4. Find the inverse of the following n × n matrix: A = 1 0 0 ... 1 2 0 ... 1 2 3 ... . . . . . . . . . 1 2 3 ... n . [ Hint : Use the algorithm for the case 3 × 3 or 4 × 4, guess the answer for the n × n matrix and prove it is indeed A-1 .] 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