# 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.

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

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

Q16:

Consider the following matrix equation:

Find the value of that results in .

Q17:

Consider the following matrix equation:

Find the value of that results in .

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, ,

Q25:

Three planes are defined by the following equations: , , and . Find their point of intersection.

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,