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.
- Created On
- August 22nd, 2017
- 6 years ago
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- 3
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- Video
- Language
- English
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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
History
August 22nd, 2017 6 years ago
Submitted by Petra Taylor
