# 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.

**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