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

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, ,

**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

**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

**Q14: **

True or False: If the equations of three nonintersecting planes are represented in the matrix form , then matrix can be inverted.

- AFalse
- BTrue

**Q15: **

True or False: The solution of the matrix equation is .

- ATrue
- BFalse

**Q18: **

True or False: In the matrix equation , the existence of a solution depends only on the matrix.

- AFalse
- BTrue

**Q19: **

True or False: In the matrix equation the value of the solution, if it exists, depends only on matrix .

- ATrue
- BFalse

**Q20: **

True or False: If the coefficient matrix is invertible, then the system of equations has a unique solution.

- ATrue
- BFalse

**Q21: **

Consider the matrix equation

Find the solution in terms of the constants and .

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

**Q22: **

Consider the matrix equation

Find the solution in terms of the constant .

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

**Q23: **

, , and are angles of a triangle. and . Find the three angles.

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

**Q24: **

Consider the matrix equation

Find the solution in terms of the constant .

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