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Determine whether the following statements are true or false and provide a justification for your response....

Determine whether the following statements are true or false and provide a justification for your response.

  1. If the coefficient matrix of a system of linear equations has a pivot in the rightmost column, then the system is inconsistent.

  2. If a system of equations has two equations and four unknowns, then it must be consistent.

  3. If a system of equations having four equations and three unknowns is consistent, then the solution is unique.

  4. Suppose that a linear system has four equations and four unknowns and that the coefficient matrix has four pivots. Then the linear system is consistent and has a unique solution.

  5. Suppose that a linear system has five equations and three unknowns and that the coefficient matrix has a pivot in every column. Then the linear system is consistent and has a unique solution.

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