# Worksheet: Solving Linear Systems with Matrix Equations

Q1:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q2:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q3:

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

• A ,
• B ,
• C ,
• D ,

Q4:

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

Q5:

Using matrix inverses, solve the following for :

• A
• B
• C
• D
• E

Q6:

Use matrices to solve the system

• A ,
• B ,
• C ,
• D ,
• E ,

Q7:

Use matrices to solve the following system of equations:

• A
• B
• C
• D
• E

Q8:

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

Q9:

Use matrices to solve the system of equations

• 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

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

Q12:

Given the following, find the matrix .

• A
• B
• C
• D

Q13:

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

• A ,
• B ,
• C ,
• D ,

Q14:

Solve for .

• A
• B
• C
• D
• E

Q15:

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

Q16:

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

Q17:

Use matrices to solve the following system of equations:

• A
• B
• C
• D
• E