MA 305 Homework 1

Due midnight on Friday, February 1,  2002

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.

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

1. Find all solutions to the given linear system.
    1.   x  +  3y =  5

      2. 3x - 4y  =  2
       
    2.    x + 4y -  z = 2

      3. -x -4y + 2z = 0
         x +4y          = 4


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.

3. Write the augmented matrix for the following linear system and write it in row echelon form.
Is the system consistent or inconsistent?
 

4. Let the matrix A be an augmented matrix for a system of linear equations.

     
    A =  [   r   s   t   0   0   ]
    [   0   r   s   t   0   ]
    [   0   0   r   s   t   ]
    [   0   0   0   r   s   ]


Find conditions on r,s and t such that

a) the matrix is in reduced row echelon form.
b) the matrix is in reduced row echelon form and the system is consistent.