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Remember that a
3 x 3
system is really three planes that are living in 3-D space...
They're actually locked into specific locations (not floating
around) and we want to find where they intersect.
But, the three planes might not
all intersect in a nice little point.
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Two of the planes
might be parallel. |
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All three planes
might be parallel. |
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Or this could
happen! |
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In all of the cases, you won't get
a single point where all three planes intersect... So, there
will be no solution.
When you are doing your
elimination method, you'll be happily going along...
And you'll add two equations
together and get a false statement like
When this happens, you'll know
that there is no solution. For
your answer, write something like
"All three planes
do not
intersect in a single point.
So, there is no solution."
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