Finding all solutions of systems of linear equations

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.

math.la.e.linsys.3x3.soln.homog.row_reduce.i

math.la.d.linsys.homog

math.la.t.linsys.homog.nontrivial

math.la.c.linsys.soln_set.vec

math.la.d.linsys.homog.trivial

math.la.d.linsys.homog.nontrivial

Created On: August 22nd, 2017; 7 years ago
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Type: Video
Language: English
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Solving homogeneous systems of equations

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.

Created On: August 25th, 2017; 7 years ago
Views: 4
Type: Video
Language: English
Content Type: text/html; charset=utf-8

A homogeneous system has a nontrivial solution if and only if it has a free variable.