If the row echelon form is not strictly triangular, then the system may also have an unique1solution.

The statement is not entirely correct. The row echelon form of a matrix does not necessarily determine the uniqueness of the solution to a system of equations.

Here's a step-by-step explanation:

1. The row echelon form of a matrix is a form that is achieved through Gaussian elimination, a method used to solve systems of linear equations. It transforms the matrix into a form where the leading coefficient (the first non-zero number from the left, also called the pivot) of each row is always to the right of the leading coefficient of the row above it.

2. A system of linear equations may have a unique solution, no solution, or infinitely many solutions. The row echelon form can help determine which of these is the case.

3. If the row echelon form of a matrix is strictly triangular (all entries below the main diagonal are zero), then the system has a unique solution. This is because each equation in the system corresponds to a row of the matrix, and a strictly triangular form means that each equation has a unique solution.

4. However, if the row echelon form is not strictly triangular, it does not necessarily mean that the system does not have a unique solution. It could still have a unique solution, no solution, or infinitely many solutions, depending on the specific system of equations.

5. To determine the number of solutions, you would need to look at the specific values in the matrix. For example, if there is a row with all zeros except for the last entry, then the system has no solution. If there is a row with all zeros including the last entry, then the system has infinitely many solutions.

In conclusion, the row echelon form can provide information about the number of solutions to a system of equations, but it does not solely determine the uniqueness of the solution.