infinite solution of matrices occur if the following conditions satisfy.
For a m*n matrix let us say 3*3 matrix.
if you reduce echelon the matrix then
- [0 0 0…0|a] where a should equal to zero should occur.
- the rank of the augmented matrix[A|b] and rank of A should be the same but their rank should be less then n rank<n.(where n is number of columns of matrix A.) (and rank is number of non zero rows in [A|b]).
- if a free variable occurs for instance if you subtract n-r where r is rank and you get 1,2 so on free variables then the matrix is bound to have infinite many solutions.
