If an elementary row operation is applied to a matrix that is in row echelon form, the resulting matrix will still be in row echelon form.

Every matrix has a unique row echelon form.

A homogeneous linear system in $$n$$  unknowns whose corresponding augmented matrix has a reduced row echelon form with  $$r$$  leading 1's has  $$n-r$$  free variables.

All leading 1's in a matrix in row echelon form must occur in different columns.

If every column of a matrix in row echelon form has a leading 1, then all entries that are not leading 1's are zero.

If a homogeneous linear system of  $$n$$  equation in  $$n$$  unknowns has a corresponding augmented matrix with a reduced row echelon form containing  $$n$$  leading 1's, then the linear system has only the trivial solution.

If the reduced row echelon form of the augmented matrix for a linear system has a row of zeros, then the system must have infinitely many solutions.

If a linear system has more unknowns than equations, then it must have infinitely many solutions

This is an example of a

Using back-substitution, calculate the solution for the REF matrix.

Johnny was using Gaussian Elimination to simplify the matrix. What did he do wrong in this step?

Jessica is simplifying the matrix using Gaussian Elimination. Did she complete the step correctly?

Which row command is an appropriate next step?

What is an appropriate first row command to solve this by Gaussian Elimination?