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spoc21
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Homework Statement
Solve the following systems and interpret the result geometrically
x - y - 2z - 3 = 0
2x - 3y - 3z + 15 = 0
x - 2y - z + 10 = 0
Homework Equations
The Attempt at a Solution
x - y - 2z - 3 = 0…………….(1)
2x - 3y - 3z + 15 = 0……….(2)
x - 2y - z + 10 = 0…………..(3)
first multiply equation (1) by -2
getting:
2x-2y-4z-6=0
Use elimination:
2x-2y-4z-6=0
-(2x - 3y - 3z + 15 = 0)
y-z-21=0
y-z=21
Elimination:
x-y-2z-3=0
-(x - 2y - z + 10 = 0)
y-z-13=0
==> y-z=13
Use elimination:
y-z=+21
y-z=13
Use elimination
(y-z=21)
-(y-z=13)
0=8
The answer is 0=number..This means that the system is inconsistent, and the planes never intersect.
I would really appreciate it if someone could take a look over my working, and point out any mistakes.
Thanks!