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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