Is the statement "Two fundamental questions about a linear system involve existence and uniqueness" true or false? Explain.

Question

Mathematics

Madelyn Stephens

26 August, 11:15

Is the statement "Two fundamental questions about a linear system involve existence and uniqueness" true or false? Explain.

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Answers (1)

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Jaidyn Vasquez · Answer 1

True

Explanation:

First of all its necessary remember that a linear system is a compound of multiple equations that involve variables.

Existence:

Depending on the number of equations and the number of variables, you could determine if the linear system has a solution or not. There are 3 possibilities:

If the linear system has more equations than variables could exist infinite answers. If the linear system has more variables than equations, it is considered an undetermined system and you neer more information to solve it. If the linear system has the same number of equations and variables, the system is consistent and has at least one solution. Uniqueness:

If possibility 3 is presented, it becomes necessary know if its the only one solution or exists more than one solution.

Rgds.