###### Exercise 3

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

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

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

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

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.

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.