22.2. Types of Matrix Forms

Try these first

1. 1.

   Define Row Echelon Form (REF).

   Hint

   Look into the properties of arranged rows.

2. 2.

   What is the leading coefficient?

   Hint

   Think about where it appears in the row.

3. 3.

   What is Row Echelon Form?

   • A form where all entries are zero
   • All non-zero rows above zero rows
   • All rows must be the same

   Hint

   Think about the arrangement of rows.

4. 4.

   Is it true that every matrix in RREF has leading ones only?

   • True
   • False

   Hint

   Consider the strict conditions of RREF.

5. 5.

   Prove whether the following matrix is in Row Echelon Form: [2 4 6] [0 1 5] [0 0 0]

   Hint

   Check the arrangement of the rows and the leading coefficients.

6. 6.

   Using the matrix [1 2 3] [2 5 4] [3 6 5], guide through the steps to convert it to Reduced Row Echelon Form.

   Hint

   Focus on achieving leading ones and clearing out columns.