Homogeneous Systems

If a system of m equations and n unknowns has all zero independent terms, it is said to be homogeneous.

It only admits the trivial solution: x1 = x2 =... = xn = 0.

The necessary and sufficient condition for a homogeneous system has solutions other than the trivial when the rank of the coefficient matrix is less than the number of unknowns, that is to say, that the determinant of the coefficient matrix is zero.

r < n

Solving Homogeneous Systems

Homogeneous System

Homogeneous System

Homogeneous System Solution

Homogeneous System

Homogeneous System

Homogeneous System Solution

System of Equations

Matrix

r = 3 n = 3

Trivial Solution


System of Solutions

Homogeneous System

Homogeneous System Solution

Homogeneous System

Homogeneous System

Homogeneous System Solution


System of Equations

Homogeneous System

r = 3 n = 3

Trivial Solution