# Worksheet: Gaussian Elimination

In this worksheet, we will practice using Gaussian elimination to get a row echelon form of a matrix and hence solve a system of linear equations.

Q1:

True or False: If a matrix is in row-echelon form, then the entry in the third row, second column must be 0.

• AFalse
• BTrue

Q2:

Using the row echelon form, check the number of solutions that the following system of linear equations has:

• AThe system has a unique solution.
• BThe system has no solutions.
• CThe system has an infinite number of solutions.

Q3:

Which of the following is the matrix in row echelon form?

• A
• B
• C
• D
• E

Q4:

Find the row echelon form of the following matrix:

• A
• B
• C
• D
• E

Q5:

The equation of a circle has the form . Hence, a circle is determined by three points. Find the equation of the circle through the points , , and by solving the equation using Gaussian elimination. Take .

• A
• B
• C
• D
• E

Q6:

Find the general solution for the system

• A
• B
• C
• D
• E

Q7:

Find the general solution for the system

• A
• B
• C
• D
• E

Q8:

Using Gaussian elimination, solve the following system of linear equations:

• A
• B
• C
• D
• E

Q9:

Which of the following is the matrix in row echelon form?

• A
• B
• C
• D
• E

Q10:

Which of the following is the matrix in row echelon form?

• A
• B
• C
• D
• E

Q11:

Using Gaussian elimination, solve the following system of linear equations:

• A
• B
• C
• D
• E