# Worksheet: Solving a System of Three Equations Using a Matrix Inverse

In this worksheet, we will practice solving a system of three linear equations using the inverse of the matrix of coefficients.

Q1:

Solve using the inverse of a matrix.

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q2:

Given that find the values of , , and .

• A, ,
• B, ,
• C, ,
• D, ,

Q3:

Given that find the values of , , and .

• A, ,
• B, ,
• C, ,
• D, ,

Q4:

Given that find the values of , , and .

• A, ,
• B, ,
• C, ,
• D, ,

Q5:

Given that

solve the following matrix equation for :

• A
• B
• C
• D
• E

Q6:

Solve the system of the linear equations , , and using the inverse of a matrix.

• A, ,
• B, ,
• C, ,
• D, ,

Q7:

Use the inverse of a matrix to solve the system of linear equations , , and .

• A, ,
• B, ,
• C, ,
• D, ,

Q8:

Use matrices to solve the following system of equations:

• A
• B
• C
• D
• E

Q9:

Consider the system of equations

Express the system as a single matrix equation.

• A
• B
• C
• D
• E

Work out the inverse of the coefficient matrix.

• A
• B
• C
• D
• E

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

• A
• B
• C
• D
• E

Q10:

Consider the system of equations

Express the system as a single matrix equation.

• A
• B
• C
• D
• E

Work out the inverse of the coefficient matrix.

• A
• B
• C
• D
• E

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

• A
• B
• C
• D
• E

Q11:

Consider the system of equations

Express the system as a single matrix equation.

• A
• B
• C
• D
• E

Work out the inverse of the coefficient matrix.

• A
• B
• C
• D
• E

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

• A
• B
• C
• D
• E

Q12:

Use matrices to solve the following system of equations:

• A
• B
• C
• D
• E

Q13:

Use the inverse matrix to solve giving your answer as an appropriate matrix.

• A
• B
• C
• D
• E