Homogeneous systems of linear equations; trivial versus nontrivial solutions of homogeneous systems; how to find nontrivial solutions; how to know from the reduced row-echelon form of a matrix whether the corresponding homogeneous system has nontrivial solutions.

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- August 25th, 2017
- 4 years ago
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##### Definition of homogeneous linear system of equations math.la.d.linsys.homog

##### Definition of trivial solution to a homogeneous linear system of equations math.la.d.linsys.homog.trivial

##### Definition of nontrivial solution to a homogeneous linear system of equations math.la.d.linsys.homog.nontrivial

##### A homogeneous system has a nontrivial solution if and only if it has a free variable. math.la.t.linsys.homog.nontrivial

##### Example of solving a 3-by-3 homogeneous system of linear equations by row-reducing the augmented matrix, in the case of infinitely many solutions math.la.e.linsys.3x3.soln.homog.row_reduce.i