MA 305 Homework 3

Due 11:59 pm on Friday, March 10, 2000

Calculations necessary for these problems may be done either by hand or with Maple. Label all problems and answers. Partial credit will only be given for included work. Solutions are to be submitted as ASCII text (.txt), Maple Worksheet (.mws), html (.html), postscipt (.ps), or portable document format (.pdf) file via WolfWare. (Please read the instructions for how to submit files.)

Questions about the assignment may be sent to the TA, Will Turner, at wjturner@math.ncsu.edu.

1. Consider the linear system

   2 x₁ - x₂ + x₃ = -1
   4 x₁ - x₂ + 4 x₃ = -2
   -2 x₁ + x₂ + 2 x₃ = -2
   1. Write the corrsponding coefficient matrix A and right-side vector b such that A x = b .
   2. Find matrices T and U such that U is in row echelon form and TA = U.

2. Find the L U factorization of the matrix A from above.

3. Use the L U factorization of A to solve the linear system given in problem 1. (Hint: use Maple command linsolve to solve a linear system.)

4. Use Cramer's rule to solve the same system.