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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.

  • A
  • B
  • C
  • D

Q7:

Given that find the matrix .

  • A
  • B
  • C
  • D

Q8:

Given that find the matrix .

  • A
  • B
  • C
  • D

Q9:

Given that solve the following equation.

  • A
  • B
  • C
  • D

Q10:

Determine given the following.

  • A
  • B
  • C
  • D

Q11:

Given that find the matrix .

  • A
  • B
  • C
  • D
  • E

Q12:

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

  • A
  • B
  • C
  • D

Q13:

Consider the matrices and . Find .

  • A
  • B
  • C
  • D

Q14:

Given that determine the matrix that satisfies the relation .

  • A
  • B
  • C
  • D

Q15:

Solve the following matrix equation.

  • A
  • B
  • C
  • 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 2 Γ— 2 matrix 𝐴 , where 𝐴  1 2 3 4  =  1 2 3 4  𝐴 , must be a combination of  1 0 0 1  and  1 2 3 4  . In other words, it must be 𝐴 = 𝑠  1 0 0 1  + 𝑑  1 2 3 4  for some numbers 𝑠 and 𝑑 . James wants to challenge this, since he see that 𝐴 =  1 2 3 4  2 produces the same product  1 2 3 4  3 when multiplied on either side. Help Daniel by finding 𝑠 and 𝑑 so that

  • A 𝑠 = 1 , 𝑑 = 3
  • B 𝑠 = 5 , 𝑑 = 2
  • C 𝑠 = 3 , 𝑑 = 1
  • D 𝑠 = 2 , 𝑑 = 5
  • E 𝑠 = 3 , 𝑑 = 6

Q20:

Given that

solve the following matrix equation for 𝑋 :

  • A 𝑋 =  1 0 βˆ’ 7 βˆ’ 3 7 3 βˆ’ 4 8 βˆ’ 2 2 βˆ’ 2 8 1 9 9 
  • B 𝑋 =  βˆ’ 1 6 9 5 9 βˆ’ 5 βˆ’ 1 2 6 βˆ’ 1 4 βˆ’ 8 
  • C 𝑋 =  5 βˆ’ 5 6 3 2 βˆ’ 2 8 4 1 βˆ’ 1 3 1 1 βˆ’ 1 6 
  • D 𝑋 =  βˆ’ 5 5 βˆ’ 6 βˆ’ 3 2 2 8 βˆ’ 4 1 1 3 βˆ’ 1 1 1 6 
  • E 𝑋 =  βˆ’ 2 1 0 2 9 βˆ’ 1 5 βˆ’ 1 0 6 8 βˆ’ 3 6 2 2 