How to compute all solutions to a general system $Ax=b$ of linear equations and connection to the corresponding homogeneous system $Ax=0$. Visualization of the geometry of solution sets. Consistent systems and their solution using row reduction.

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- August 22nd, 2017
- 5 years ago
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##### 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

##### Definition of homogeneous linear system of equations math.la.d.linsys.homog

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

##### Parametric vector form of the solution set of a system of linear equations math.la.c.linsys.soln_set.vec

##### 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