MA 305 Homework 4

Due 11:59 pm on Friday April 19,  2002

Calculations necessary for these problems may be done either by hand or with Maple. Solutions are to be submitted as a ASCII text (.txt) or Maple Worksheet (.mws) (version 7 or lower),  file via WolfWare.

If you use Microsoft word, please save your file as ascii text with a .txt extension before submitting the file.

Submitted files should have either .txt or .mws extensions. This makes the grader's life much easier.

Incorrectly submitted files will result in NO CREDIT, so be sure the file you submit is readable in a text editor or Maple. If you are using Windows, check text files using notepad to make sure it looks readable.

Show your work for full credit. This means show all of your maple commands or if done by hand show most of the intermediate steps so we know how you arrived at your answer.

You must write up your own homework.  You may work together in the formulation of your answers, but you must type your  own file(i.e. no copying and pasting either).

Put your name and the names of all the people you worked with at the beginning of your submission file.

Questions about the assignment may be sent to the TA, George Yuhasz at  gyuhasz@math.ncsu.edu

1. Find a basis for the column space of A.
2. Find a basis for the row space of A.
3. What is the rank of A.
4. True or False, for any b in R³ there is a solution to Ax=b? Explain.
5. True or False, for any b in R³ there is at most one solution to Ax=b? Explain.

Compute the following

1. The scalar products: u^Tv, u^Tw, v^Tw.
2. For each pair of vectors, are they orthogonal?
3. The euclidean norm: ||v||, ||w||, ||u-v||.
4. The angle between v and w.
5. The projection of w onto v.
6. The orthogonal complement of S=span_R(u,v,w).

1. Compute b^{^} , the orthogonal projection of b onto span_R(v,w,z).
2. Compute the infinity norm and the Manhatten norm of b-b^{^}.