# Worksheet: Homogeneous Systems of Linear Equations

In this worksheet, we will practice finding the solution of a homogeneous system of linear equations and expressing the general solution in case of an infinite number of solutions.

Q1:

Which of the following systems of equations is homogeneous?

• A,
• B,
• C,
• D,

Q2:

Find the value of that would make the equations , , and have a solution other than zero.

Q3:

Find all the solutions to the system of equations , .

• AThe system has no solution.
• B, , where is an integer
• C,
• DThe system only has a trivial solution: , .
• E, , where is an integer

Q4:

Find all the solutions of the system of equations , , .

• AThe system only has a trivial solution , , .
• B, , , where is an integer
• C, ,
• DThe system has no solution.
• E, , , where is an integer

Q5:

Find all the solutions of the system of equations , , .

• AThe system has no solution.
• B, ,
• C, , , where is an integer
• DThe system only has a trivial solution , , .
• E, , , where is an integer