Step 1 :Given the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, we have the following matrix: \[\left[\begin{array}{lll|l} 1 & 0 & 0 & 1 \ 0 & 1 & 0 & 4 \ 0 & 0 & 0 & 0 \end{array}\right]\]
Step 2 :From the matrix, we can see that the system has infinitely many solutions because the third row of the matrix is all zeros, which means that the third variable, z, is free to take any value.
Step 3 :The solutions to the system can be expressed as \[(x, y, z) = (1, 4, t)\], where t is any real number.