Get this system in triangular form. Try multiplying Row 3 by 2, then add that to Row 2. Follow this by multiplying Row 3 by -7, then adding that to Row 1. Rewrite the original Row 1 and the two new equations. One more step to get it to triangular form. Can you do it?
Answer
(-3, 3, 0)
Example 4
Solve this system of equations using Gaussian Elimination.
x – y – z = 4 2x – 2y – 2z = 8 5x – 5y – 5z = 20
Hint
Do you notice anything yet? If not, try multiplying Row 1 by -2, then add Row 1 and Row 2.
Answer
Infinitely many solutions.
Example 5
Solve this system of equations using Gaussian Elimination.