# Worksheet: Solving Linear Systems with Matrix Equations

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 .

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• E

Q3:

Using matrix inverses, solve the following for :

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• E

Q4:

Consider the system of equations

Express the system as a single matrix equation.

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• B
• C
• D
• E

Write down the inverse of the coefficient matrix.

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• B
• C
• D
• E

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

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• B
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• D
• E

Q5:

Use matrices to solve the system of equations

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• 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:

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• 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:

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• 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.

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• 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 .

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