MAS
Final-ex

# B obtain a basis for w hint use the coordinate

• Notes
• 7

This preview shows page 7. Sign up to view the full content.

(b) Obtain a basis for W. (Hint: Use the coordinate mapping with respect to the natural basis for P 2 to obtain an equivalent problem in 3 . Solve that problem and translate the results to the polynomial space. Observe that the linear equation you have to solve is the one giving the defining condition on the members of W.) 7. (7 pts.) Let T: P 2 P 2 be the function defined by the rule T(p) = p - 2p , where the primes denote differentiation with respect to t. (a) Verify that T is a linear transformation. (You need only quote the appropriate properties of differentiation.) (b) Obtain the matrix [T] B , where B = {1, 1 + t, 1 + t + t 2 } is an off the wall basis for P 2 . (c) What can you tell about the dimensions of the kernel and the range by using the matrix [T] B ??
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