Is the statement A consistent system of linear equations has one or more solutions true or false? Explain.
True, a consistent system is defined as a system that has at least one solution.
The statement A consistent system of linear equations has one or more solutions is true.
A linear system of equations is said to be consistent if it has at least one solution. This means that the system of equations can be solved to find values for the variables that satisfy all the equations simultaneously.
If a system of equations is inconsistent, it means that there are no values of the variables that can satisfy all the equations. In other words, the system has no solution.
However, it is possible for a system of equations to have more than one solution, which is known as a dependent system. In this case, the equations are not independent and can be derived from each other. But the fact remains that the system is still consistent, as it has at least one solution.
Therefore, the statement A consistent system of linear equations has one or more solutions is true.
More Answers:
Understanding the Solution Set for Equations with 3 Variables: Finding Specific SolutionsMastering Linear System Solutions with Row Reduction Algorithm: A Comprehensive Guide
Mastering Linear Algebra: Understanding Multiple Reduced Echelon Forms for Matrix Manipulation