SOLUTION: This is the second part to my first question. a) While using the Gaussian method you get [0 0 0 5] as a row in your augmented matrix. What can you conclude about the system of e

Question 985516: This is the second part to my first question.
a) While using the Gaussian method you get [0 0 0 5] as a row in your augmented matrix. What can you conclude about the system of equations you are dealing with?
b) What if you get [0 0 0 0] as a row?
The system is:
a) solvable , b) inconsistent , c) dependent
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
[0 0 0 5] means we have 0x+0y+0z = 5. The zeros are the coefficients to x,y,z

But there are no solutions to 0x+0y+0z = 5 because it becomes 0+0+0=5 which becomes 0 = 5. It's always false. There are no solutions. This system is inconsistent.

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[0 0 0 0] means 0x+0y+0z = 0 which ultimately leads to 0 = 0. It's always true, so there are solutions, and this system is consistent and dependent.
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