Worksheet: Reduced Row Echelon Form
In this worksheet, we will practice identifying the reduced row echelon form of a matrix and using Gauss-Jordan elimination to get it and hence solving a system of linear equations.
Give the sum of all the pivot entries in the following matrix:
Describe the row switches which are necessary to put the following matrix into echelon form:
- AWe swap rows 1 and 3, and then rows 2 and 4.
- BThe matrix is already in echelon form; we do not need to swap any rows.
- CWe swap rows 1 and 3, and then rows 2 and 4, and finally rows 3 and 4.
- DWe swap rows 2 and 4, and then rows 2 and 1, and finally rows 2 and 3.
- EWe swap rows 2 and 4, and then rows 1 and 3, and finally rows 2 and 3.
State whether the following matrix is in echelon form:
- AThe matrix is in echelon form.
- BThe matrix is not in echelon form.