Is the statement Two fundamental questions about a linear system involve existence and uniqueness true or false? Explain.
True, because two fundamental questions address whether the solution exists and whether there is only one solution.
The statement Two fundamental questions about a linear system involve existence and uniqueness is true.
Existence and uniqueness are considered to be the most significant properties of a linear system. The existence question involves whether or not a solution exists for a given linear system. A system could have one solution, multiple solutions or no solution at all. The uniqueness question, on the other hand, is concerned with whether or not the solution is unique for the given system. If a linear system has only one solution, it is considered to be unique.
Thus, when solving a linear system, it is crucial to determine if the system has both existence and uniqueness. If it has existence but does not have uniqueness, there could be more than one solution to the system. Alternatively, if it does not have existence, then there will be no solution to the system. Therefore, for the statement Two fundamental questions about a linear system involve existence and uniqueness is valid and true.
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