Question

Suppose the matrix representing a system of difference equations contains a row of zeros. What does this imply about the system?

Answer 1

Answer:

dimension-crushing transformation.

Step-by-step explanation:

A dimension-crushing transformation represents a matrices of all zero vector element in it (row or column).

For instance, a three-dimensional matrix with an all zero row will take three-dimensional vectors.

A dimension-crushing transformation matrices have no inverse.

we can as well conclude that the corresponding matrices have a determinant of zero (and it's obvious from the way the determinant is calculated that this is so for matrices that are cross-cut by an all-zero row or column).

So all of this gives you a whole new geometric view on systems of linear equations.

reference: https://math.stackexchange.com/