# Worksheet: Finding an Unknown Variable in a Matrix

Q1:

If , where what are the values of and ?

• 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 , ,
• E , ,

Q4:

Given that find the values of , , and .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q5:

Let , and . Find and satisfying such that for some number . Also give the number .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q6:

Given that find , , and .

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q7:

Determine the values of , , , and that satisfy the given equation where is the zero matrix of order .

• A , , ,
• B , , ,
• C , , ,
• D , , ,

Q8:

Given that what are the values of , , and ?

• A , ,
• B , ,
• C , ,
• D , ,

Q9:

Write the matrix in the form , where , , , and are real numbers that you should find.

• A
• B
• C
• D

Q10:

Let and . Is it possible to choose a value for so that ? If so, what is this value?

• AThere is a possible choice for . .
• BThere is a possible choice for . .
• CThere is a possible choice for . .
• DThere is no possible choice for .
• EThere is a possible choice for . .

Q11:

Consider the shown matrices Is it possible to choose such that ? If so, what should be equal to?

• A yes,
• B no, there is no possible choice for
• C yes,
• D yes,
• E yes,

Q12:

Consider the shown matrices and . If , what are the values of and ?

• A ,
• B ,
• C ,
• D ,

Q13:

Given that where is the unit matrix, determine the value of .