AMS 476 : TA Applied Linear Algebra

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Applying Gauss's Method to any matrix always yields Echelon Form.

Gauss's Method: If a linear system is changed to another by one of these operations

  1. an equation is swapped with another
  2. an equation has both sides multiplied by a nonzero constant
  3. an equation is replaced by the sum of itself and a multiple of another

then the two systems have the same set of solutions.

Solution sets look something like:

x y z
General
=
1 0 0
Particular
+
-1/3 2/3 1 z
Homogeneous