The forms of each of the matrices depicts how the row and column elements of the matrices are arranged
The matrix A is given as:
[tex]\left[\begin{array}{cccc}4&11&2\\0&-5&8\\0&0&-2\end{array}\right]\left[\begin{array}{c}-6&7&3\end{array}\right][/tex]
The elements on the leading diagonals are: 4, -5 and -2
The elements under the leading diagonals are 0, 0 and 0
When the elements under the leading diagonals are 0, then the augmented matrix is row echelon form
The matrix B is given as:
[tex]\left[\begin{array}{cccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\left[\begin{array}{c}-6&3&3\end{array}\right][/tex]
The elements on the leading diagonals are: 1, 1 and 1
All other elements in the matrix are 0's
When the elements on the leading diagonals are 1's, and other elements are 0's, then the augmented matrix is reduced row echelon form
The matrix C is given as:
[tex]\left[\begin{array}{cccc}1&0&3\\0&6&0\\7&0&1\end{array}\right]\left[\begin{array}{c}-6&8&13\end{array}\right][/tex]
The above matrix is neither in row echelon form nor in reduced row echelon form, because it does not satisfies the condition of both forms of matrices
Read more about augmented matrices at:
https://brainly.com/question/11392945
