I'm studying System of linear equations.
Ax=b, it is said that the system can behave in 3 ways.
- No solution
- Unique solution
- Infinitely many solutions
And according to Wikipedia page,
Usually, a system with fewer equations than unknowns has infinitely many solutions, but it may have no solution. Such a system is known as an underdetermined system.
Usually, a system with the same number of equations and unknowns has a single unique solution.
Usually, a system with more equations than unknowns has no solution. Such a system is also known as an overdetermined system.
I think the word
Usually implies that the system can behaves in 3 ways for any arbitrary matrices(it does not care the matrix is a square matrix or non-square matrix).
I want to know the possible behaviors when the matrix A is non-square.
My questions are
- Can non-square matrices(m < n) have a unique solution(unknowns > equations)?
- Can non-square matrices(m > n) have infinitely many solutions(unknowns < equations)?