Page 377 - 35Linear Algebra
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G.3 Vectors in Space n-Vectors 377
• For three equations, most often their intersection will be a single
point so the solution will then be unique:
• Of course stuff can go wrong. Two different looking equations could
determine the same plane, or worse equations could be inconsistent. If
the equations are inconsistent, there will be no solutions at all. For
example, if you had four equations determining four parallel planes the
solution set would be empty. This looks like this:
G.3 Vectors in Space n-Vectors
Review of Parametric Notation
The equation for a plane in three variables x, y and z looks like
ax + by + cz = d
where a, b, c, and d are constants. Lets look at the example
x + 2y + 5z = 3 .
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