Gauss 2

Homework

Solving a System Using Gaussian Elimination 

Write the system of equations in an augmented matrix.  Use elementary row operations to get the matrix into row-echelon form or reduced-row echelon form to solve the system.

#1) 3x + 3z = 0
      2x + 2y = 2
      3y + 3z = 3

#2) x + 3y - 3z = 12
     3x - y + 4z = 0
     -x + 2y - z = 1

#3) x + y + z = 3
      2x - y - z = 0
      x + 2y - z = -1

#4)  (1/2)x + (1/3)y = 4
       (1/2)y - (1/4)z = 1
       (1/4)x + (1/2)z = 5

#5)  (1/3)x - (1/3)z = -2
       (1/6)y + (1/3)z = 7
       (2/3)x + (1/4)y = 9


Answers
#1)  (0, 1, 0)
#2)  (3, 1, -2)
#3)  (1, 0, 2)
#4)  (4, 6, 8)
#5)  (9, 12, 15)