MA305 HW #1

Due January 31st at 23:45:00. Submit a postscript or ASCII text file electronically via Wolfware @ http://submit.ncsu.edu/. Email submissions will not be accepted.

Problem #1

Demonstrate how to solve the following linear system by direct manipulation of the equations.

                          x + 7 y = 4
                         -2 x  - 9 y = 3

Is this system consistent or inconsistent? Why?

Problem #2

(a) Construct the augmented matrix for the linear system in problem #1. (b) Use Gaussian elimination to put the matrix into row echelon form. (c) Translate the matrix back into a linear system and solve it via "back substitution".

Problem #3

Write the augmented matrix for the following linear system and find its row echelon form.

                      x1 - 6 x2  = 5
                      x2 - 4 x3 + x4 = 0
                     -x1 + 6 x2 + x3 + 5 x4 = 3
                     -x2 + 5 x3 + 4 x4 = 0

Is the system consistent or inconsistent?

Problem #4

Find two examples of linear systems of three equations in three variables which have unique solutions. Find two with infinitely many solutions. Find two with no solutions.

John Paul May

Last modified: Tue Jan 23 16:51:02 EST 2001