MA 305 Homework 2

Due 11:59 pm on Friday, February 25, 2000

Calculations necessary for these problems may be done either by hand or with Maple. 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. Let

   A =	[ 1 2 3 ] [ 3 1 3 ] [ 2 1 4 ]

   Find

   1. 3 A + 5 A²
   2. A⁴ - A³ + 2 A² - A + 4 I₃

2. Let

   A =

   [ 1 3 ] [ 1 4 ] [ 2 1 ]

   and

   B =

   [ 1 1 3 ] [ 2 1 2 ] [ 4 2 1 ]

   If possible, determine the following. If the calculation is not possible explain why not.

   1. (AB)^T
   2. A^TB^T
   3. BB^T
   4. AA^T
   5. A^TA
   6. B^TA^T

3. Find the inverse of the following matrix:

   [ 1 0 0 0 ] [ 0 3 0 0 ] [ 2 0 3 0 ] [ 4 5 0 1 ]

4. Find the inverse of the following matrix, where a and b are non-zero.

   [ 1 b 0 0 ] [ a 1 b 0 ] [ 0 a 1 b ] [ 0 0 a 1 ]