Two fundamental questions about a linear system involve existence and uniqueness (T/F)
True
True. Two fundamental questions when dealing with a linear system of equations involve the concepts of existence and uniqueness. These questions are:
1. Does a solution to the linear system exist?
2. If a solution exists, is it unique?
Existence refers to whether or not a solution can be found for the given system of linear equations. It is determined by analyzing the coefficients and constants in the equations.
Uniqueness, on the other hand, refers to whether a solution, if it exists, is the only solution. In other words, it asks whether there is more than one solution or if there is a particular unique solution that satisfies the linear system.
These two concepts are essential in studying linear systems as they help determine the nature and properties of solutions, along with providing insights into the behavior of the system.
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