Suppose a linear system of equations has 2012 equations and 2013 unknowns. Answer the
following questions:
� Can the system be inconsistent?
� Can the system have a unique solution?
� Can the system have infinitely many solutions?
To determine whether the system of equations can be inconsistent, we need to compare the number of equations to the number of unknowns. In this case, we have 2012 equations and 2013 unknowns.
1. Can the system be inconsistent?
To determine if the system can be inconsistent, we need to check if the number of equations is less than the number of unknowns. Since we have 2012 equations and 2013 unknowns, the system can be inconsistent.
2. Can the system have a unique solution?
To determine if the system can have a unique solution, we need to check if the number of equations is equal to the number of unknowns. Since we have 2012 equations and 2013 unknowns, the system cannot have a unique solution.
3. Can the system have infinitely many solutions?
To determine if the system can have infinitely many solutions, we need to check if the number of equations is greater than the number of unknowns. Since we have 2012 equations and 2013 unknowns, the system can have infinitely many solutions.
In summary:
- The system can be inconsistent because the number of equations is less than the number of unknowns.
- The system cannot have a unique solution because the number of equations is not equal to the number of unknowns.
- The system can have infinitely many solutions because the number of equations is greater than the number of unknowns.