In this worksheet, we will practice expressing a system of linear equations in matrix form and solving this system by the matrix inversion method.

**Q1: **

Given find the matrix .

- A
- B
- C
- D

**Q2: **

Solve for .

- A
- B
- C
- D
- E

**Q3: **

Using matrix inverses, solve the following for :

- A
- B
- C
- D
- E

**Q4: **

Consider the system of equations

Express the system as a single matrix equation.

- A
- B
- C
- D
- E

Write down 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

**Q5: **

Use matrices to solve the system of equations

- A
- B
- C
- D
- E

**Q6: **

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

**Q7: **

Use matrices to solve the following system of equations:

- A
- B
- C
- D
- E

**Q8: **

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

**Q9: **

Use matrices to solve the following system of equations:

- A
- B
- C
- D
- E

**Q10: **

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

- A , ,
- B , ,
- C , ,
- D , ,

**Q11: **

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

- A , ,
- B , ,
- C , ,
- D , ,

**Q12: **

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

- A ,
- B ,
- C ,
- D ,

**Q13: **

Consider the simultaneous equations

Express the simultaneous equations as a single matrix equation.

- A
- B
- C
- D
- E

Write down 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

**Q14: **

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

**Q15: **

Given that the solution set of the equation is , use matrices to find the constants and .

- A ,
- B ,
- C ,
- D ,

**Q16: **

Use matrices to solve the system

- A ,
- B ,
- C ,
- D ,
- E ,

**Q17: **

Solve this system of equations using the inverse matrix

Give your solution as an appropriate matrix whose elements are expressed in terms of , , , and .

- A
- B
- C
- D
- E