# Worksheet: Finding an Unknown Matrix

In this worksheet, we will practice using operations on matrices and matrix inversion to find an unknown matrix as an introduction to solve a system of linear equations.

Q1:

Consider the matrices Find the matrix that satisfies the equation .

• A
• B
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• D

Q2:

Given that what are and ?

• A ,
• B ,
• C ,
• D ,

Q3:

Adam guesses that any matrix , where , must be a combination of and . In other words, it must be for some numbers and . Ramy wants to challenge this, since he see that produces the same product when multiplied on either side. Help Adam by finding and so that

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• E

Q4:

Given that find the values of and that satisfy , where is the zero matrix of order and is the unit matrix of order .

• A ,
• B ,
• C ,
• D ,

Q5:

Given that find the values of and .

• A ,
• B ,
• C ,
• D ,

Q6:

Given that find the matrix .

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• D

Q7:

Given that find the matrix .

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• D

Q8:

Determine , given that

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• D

Q9:

Solve the matrix equation .

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• E

Q10:

Find the matrix that satisfies the equation .

• A
• B
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• D

Q11:

Given that

solve the following matrix equation for :

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• E

Q12:

Given that find the matrix .

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• E

Q13:

Given that solve the equation

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• D

Q14:

Consider the matrices Determine the matrix that satisfies .

• A
• B
• C
• D

Q15:

Consider the matrices and : Find .

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Q16:

Given that determine the matrix that satisfies the relation .

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• D

Q17:

Let and . Solve the matrix equation for the matrix .

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• E

Q18:

Consider the matrices Find the matrix that satisfies the equation .

• A
• B
• C
• D

Q19:

Consider the matrices Find the matrix that satisfies the equation .

• A
• B
• C
• D

Q20:

Given that what are and ?

• A ,
• B ,
• C ,
• D ,

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