# Worksheet: The General Solution of a System of Linear Equations

In this worksheet, we will practice finding the general solution of a system of linear equations whether it has a unique solution, an infinite number of solutions, or no solution.

Q1:

Find the general solution to the system of equations associated with the following augmented matrix:

• A, , , ,
• B, , , ,
• C, , , ,
• D, , , ,
• E, , , ,

Q2:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q3:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q4:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q5:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q6:

Find the general solution of the system with the augmented matrix

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q7:

Find the general solution of the system with the augmented matrix

• A, , , where
• B, , , where
• C, , , where
• D, , , where
• E, , , where

Q8:

Which matrix below would you row-reduce to solve the following system of equations:

• A
• B
• C
• D

Q9:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q10:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q11:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q12:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q13:

Find the general solution to the linear system

• A
• B
• C
• D
• E

Q14:

Consider the matrix

Find the matrix with the smallest positive integer entries, ,such that

• A
• B
• C
• D
• E

Find the matrix with the smallest non-zero positive integer entries, , such that

• A
• B
• C
• D
• E

Q15:

Find the solution of the system of equations , , , giving your answer in terms of an arbitrary real number if necessary.

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q16:

Find the solution of the system of equations , , , giving your answer in terms of an arbitrary real number if necessary.

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,