The uniqueness of the a given linear system of equations can be checked when we write it in the matrix form, i.e. Ax = b.
UNIQUENESS: When the rank of the matrix A and b is equivalent to the number of variables, we have a unique solution.
INFINITE SOLUTIONS: When the rank of A and b is equal, but less than the number of variables, we get many solutions.
NO SOLUTION: When the rank of A is less than the number of variables, but the rank of b is equal to the number of variables.
keenan
@rajas139 Yep, definitely. For problems in graphics, it's also important to think geometrically about why there are/are not solutions. For instance, what solutions are in the null space of the matrix? Should that solution be in the null space? Or is it a numerical artifact? Etc.
The uniqueness of the a given linear system of equations can be checked when we write it in the matrix form, i.e. Ax = b.
UNIQUENESS: When the rank of the matrix A and b is equivalent to the number of variables, we have a unique solution. INFINITE SOLUTIONS: When the rank of A and b is equal, but less than the number of variables, we get many solutions. NO SOLUTION: When the rank of A is less than the number of variables, but the rank of b is equal to the number of variables.
@rajas139 Yep, definitely. For problems in graphics, it's also important to think geometrically about why there are/are not solutions. For instance, what solutions are in the null space of the matrix? Should that solution be in the null space? Or is it a numerical artifact? Etc.