Answer:
A) No
Explanation:
A system is consitent if it has an solution, or many solutions.
If it ends at a division by 0, or 0 = constant(different than 0), the system is inconsistent.
Let's solve this system
x1 + x2 + x3 = 7
x1 - x2 + 2x3 = 7
2x1 + 3x3 = 15
From the first equation
x1 + x2 + x3 = 7
x3 = 7 - x1 - x2
Replacing in the other equations:
In the second
x1 - x2 + 2x3 = 7
x1 - x2 + 2(7 - x1 - x2) = 7
x1 - x2 + 14 - 2x1 - 2x2 = 7
-x1 - 3x2 = -7
In the third
2x1 + 3x3 = 15
2x1 + 3(7 - x1 - x2) = 15
2x1 + 21 - 3x1 - 3x2 = 15
-x1 - 3x2 = - 6
So we have the following system now:
-x1 - 3x2 = -7
-x1 - 3x2 = - 6
Multiplying the second equation by -1, and adding both equations
-x1 - 3x2 = -7
x1 + 3x2 = 6
0 = -1
This is something that is false, so the system is inconsistent.
The correct answer is:
A) No