# Definition of trivial solution to a homogeneous linear system of equations

math.la.d.linsys.homog.trivial

# 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.d.linsys.homog.nontrivial
Created On
August 22nd, 2017
7 years ago
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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.

##### math.la.e.linsys.3x3.soln.homog.row_reduce.i
Created On
August 25th, 2017
7 years ago
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4
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English
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# Homogeneous Systems of Equations - A First Course in Linear Algebra

In this section we specialize to systems of linear equations where every equation has a zero as its constant term. Along the way, we will begin to express more and more ideas in the language of matrices and begin a move away from writing out whole systems of equations. The ideas initiated in this section will carry through the remainder of the course.