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, ,