Di¤erential Equations and Matrix Algebra I (MA 221), Fall Quarter, 1999-2000
WorkSheet 1
1) Use the Gaussian Elimination process (ie be very systematic) to solve
x + 2y + z
=1
2x + 6y + 5z = 6
x + 8y + 14z = 21
2) Solve and describe the solution set (if it exists) for each of the following.
x + 2y = 0
x + 2y = 1
x + 2y = ¡2
x + 2y
2x + 4y = 0
2x + 4y = 2
2x + 4y = ¡4
2x + 4y
=5
=2
3) Write the three systems as one augmented system and then apply Gaussian Elimination
to the augmented system. Note that this augmented system will have 3 rows and 6 columns.
x + 2y + 2z = 1
x + 2y + 2z = 0
x + 2y + 2z = 0
¡y ¡ z
=0
¡y ¡ z
=1
¡y ¡ z
=0
2x + z
=0
2x + z
=0
2x + z
=1