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Worksheet: Multiplying Matrices

Q1:

Determine the values of , , and that satisfy the following:

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

Q2:

Determine the values of , , and that satisfy the following:

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

Q3:

Determine the values of , , and that satisfy the following:

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

Q4:

Determine the values of , , and that satisfy the following:

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

Q5:

Given that find the value of .

  • A
  • B
  • C
  • D9

Q6:

Given that find the value of .

  • A
  • B
  • C
  • D

Q7:

Let 𝐢 =  1 2 3 4  , 𝐴 =  π‘Ž 𝑏 𝑐 𝑑  .

Verify that if matrix 𝐴 satisfies 𝐴 𝐢 = 𝐢 𝐴 , then 𝑐 = 3 2 𝑏 and 𝑑 = π‘Ž + 3 2 𝑏 . Find matrices 𝐷 and 𝐸 so that 𝐴 = π‘Ž 𝐷 + 𝑏 𝐸 , and then use this to find 𝑠 and 𝑑 so that 𝐴 = 𝑠  1 0 0 1  + 𝑑  1 2 3 4  .

  • A 𝐷 =  1 2 3 4  , 𝐸 =  0 1 2 3 2 3 ο₯ , 𝑠 = π‘Ž + 𝑏 2 , 𝑑 = 𝑏 2 .
  • B 𝐷 =  1 2 3 4  , 𝐸 =  0 1 3 2 3 2 ο₯ , 𝑠 = π‘Ž βˆ’ 𝑏 2 , 𝑑 = 𝑏 2 .
  • C 𝐷 =  1 0 0 1  , 𝐸 =  0 1 2 3 2 3 ο₯ , 𝑠 = π‘Ž + 𝑏 2 , 𝑑 = 𝑏 2 .
  • D 𝐷 =  1 0 0 1  , 𝐸 =  0 1 3 2 3 2 ο₯ , 𝑠 = π‘Ž βˆ’ 𝑏 2 , 𝑑 = 𝑏 2 .
  • E 𝐷 =  1 0 0 1  , 𝐸 =  0 1 3 2 3 2 ο₯ , 𝑠 = π‘Ž + 𝑏 2 , 𝑑 = 𝑏 2 .

Q8:

Find the values of π‘₯ and 𝑦 given the following.

  • A π‘₯ = 7 , 𝑦 = βˆ’ 1 2
  • B π‘₯ = 1 8 , 𝑦 = βˆ’ 4 0
  • C π‘₯ = 5 , 𝑦 = βˆ’ 4 0
  • D π‘₯ = 5 , 𝑦 = 0

Q9:

Find the values of π‘₯ and 𝑦 given the following.

  • A π‘₯ = βˆ’ 1 8 , 𝑦 = 1 2
  • B π‘₯ = βˆ’ 1 3 , 𝑦 = 3 6
  • C π‘₯ = βˆ’ 2 , 𝑦 = 3 6
  • D π‘₯ = βˆ’ 2 , 𝑦 = 4

Q10:

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

  • A ,
  • B ,
  • C ,
  • D ,