22.4.1. Method 1: Echelon Form

Try these first

1. 1.

   Define Row Echelon Form.

   Hint

   Think about how rows are organized.

2. 2.

   What are the three elementary row operations?

   Hint

   These operations are used to manipulate matrices.

3. 3.

   What is the first step to find the rank of a matrix using Echelon Form?

   Hint

   Remember the purpose of Echelon Form.

4. 4.

   When a matrix is in REF, how do you determine its rank?

   Hint

   What remains after you've manipulated the matrix?

5. 5.

   Given the matrix B: [1 0 2; 0 0 0; 3 1 4], find its rank using Echelon Form.

   Hint

   Focus on creating a leading 1 in the first pivot position.

6. 6.

   If we have a 5x3 matrix where all rows are multiples of the first row, what is its rank and why?

   Hint

   Think about independence and what it means for the rows.