# Worksheet: Finding an Unknown Matrix

Q1:

Consider the following matrices. Find the matrix that satisfies the equation .

• A
• B
• C
• D

Q2:

Consider the following matrices. Find the matrix that satisfies the equation .

• A
• B
• C
• D

Q3:

Consider the following matrices. Find the matrix that satisfies the equation .

• A
• B
• C
• D

Q4:

Given that what are and ?

• A ,
• B ,
• C ,
• D ,

Q5:

Given that what are and ?

• A ,
• B ,
• C ,
• D ,

Q6:

Find the matrix that satisfies the following equation.

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• D

Q7:

Given that find the matrix .

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• D

Q8:

Given that find the matrix .

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• D

Q9:

Given that solve the following equation.

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• D

Q10:

Determine given the following.

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Q11:

Given that find the matrix .

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• D
• E

Q12:

Consider the matrices , , and . Determine the matrix that satisfies .

• A
• B
• C
• D

Q13:

Consider the matrices and . Find .

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• C
• D

Q14:

Given that determine the matrix that satisfies the relation .

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• D

Q15:

Solve the following matrix equation.

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• D
• E

Q16:

Given that find the values of and .

• A ,
• B ,
• C ,
• D ,

Q17:

Given that find the values of and .

• A ,
• B ,
• C ,
• D ,

Q18:

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 ,

Q19:

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

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• E

Q20:

Given that

solve the following matrix equation for :

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• E