# 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.

Q1:

Is the matrix in the reduced echelon form?

• AYes
• BNo

Q2:

Transform the matrix to row-reduced echelon form.

• A
• B
• C
• D
• E

Q3:

Is the matrix in the reduced echelon form?

• ANo
• BYes

Q4:

Is the matrix in row-reduced echelon form?

• AYes
• BNo

Q5:

Reduce the matrix to obtain its row-reduced echelon form and then list the pivot columns.

• A, pivot columns: 1, 3, and 4
• B, pivot columns: 1, 2, and 3
• C, pivot columns: 2, 3, and 4
• D, pivot columns: 1, 2, and 4
• E, pivot columns: 1, 2, 3, and 4

Q6:

Reduce the matrix to obtain its row-reduced echelon form, and then list the pivot columns.

• A, pivot columns: 1, 2, and 3
• B, pivot columns: 1 and 2
• C, pivot columns: 1, 2, and 3
• D, pivot columns: 1 and 2
• E, pivot columns: 1, 2, and 3

Q7:

Give the sum of all the pivot entries in the following matrix:

Q8:

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.

Q9:

State whether the following matrix is in echelon form:

• AThe matrix is in echelon form.
• BThe matrix is not in echelon form.