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If a linear system has the same number of equations and variables, then it must have a unique solution.

True or false

User Richard
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1 Answer

3 votes

Answer:

The given statement is false.

Explanation:

We are given the following statement:

"If a linear system has the same number of equations and variables, then it must have a unique solution."

The given statement is false because If a linear system has the same number of equations and variables, then it may have unique solution, no solution or infinitely many solution.

There could be three types of solution

  • no solution,
  • unique solution and
  • infinitely many solutions,

depending on the augmented matrix and coefficient matrix of the linear system.

User Luiz Rossi
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