MA 305 Homework 1

Due midnight on Friday, February 4, 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. Find all solutions to the given linear system.

   1.   x - 2 y - z = 3
        3 x - 6 y - 5 z = 3
        2 x - y + z = 0
   2.   x + 2 y - z + 2 w + v = 2
        - x - 2 y + z + 4 w + 3 v = 6
        2 x + 4 y - 3 z + 2 w = 3
        - 3 x - 6 y + 2 z + 3 v = 9
   3.   x + y = 3
        2 x - y = 0
        x - 2 y = -1

2. Find all the values of a for which the resulting linear system has (a) no solutions, (b) a unique solution, and (c) infinitely many solutions.

   x + y + z = 3
   x + 3 y + z = 2
   x + (a²-1) y + z = a
   

3. Find an equation relating a, b, and c so that the linear system

   2 x - y + 3 z = a
   3 x + 5 y - 2 z = b
   x + 4 y - 3 z = c
   

   is consistent for any values of a, b, and c that satisfy that equation.

4. If

   A =	[		1		1		3		2		5		]
   	[		2		1		4		3		1		]
   	[		1		2		5		1		2		]
   	[		1		3		1		4		2		]

   find a matrix C in reduced row echelon form that is row equivalent to A.