The following augmented matrix is in row echelon form and belongs to some
non-homogeneous linear system:
\begin{bmatrix}a&b&c&|d\\0&e&f&|g\\0&0&h&|i\end{bmatrix}
(The entries a, e, h need not be leading entries of the row echelon form.)
Given that the matrix above is a non-homogenoeus system, am I right in assuming that d,g,i≠0? or as long as either one d,g,i is non zero, then the matrix is considered non-homogeneous system?
Best Answer
The second statement is correct: if at least one of $d,g,i$ is non-zero, then the associated system of linear equations is a non-homogeneous system.