- #1
MurdocJensen
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When I realize that I am going to have a singular matrix (after exhausting row swap options and maybe even some elimination steps) what about the matrix tells me whether or not I can have a general solution?
A singular system is a system of equations where there is no unique solution. This means that there are either infinitely many solutions or no solutions at all.
A system is singular if the determinant of its coefficient matrix is equal to zero. This means that the system has either no solutions or infinitely many solutions.
Yes, a singular system can have infinitely many solutions. This occurs when the equations in the system are not independent and are essentially describing the same relationship.
A singular system has either infinitely many solutions or no solutions, while a system with no solution has no solutions at all. In other words, a singular system has some sort of solution, while a system with no solution has no solution at all.
A singular system cannot be solved using traditional methods, such as substitution or elimination. Instead, it can be solved by finding the general solution, which represents all possible solutions for the system. This can be done by setting one variable as a parameter and expressing the other variables in terms of that parameter.