Worksheet: Constructing Matrices

In this worksheet, we will practice constructing and identifying a matrix by using the relation between its elements (entries) and their order (element location).

Q1:

Which of the following is the matrix 𝐴 = 𝑎 𝑖 𝑗 , where 𝑖 = 1 and 𝑗 = 1 , 2 ?

  • A ( 𝑎 𝑎 ) 1 2 1 1
  • B 𝑎 𝑎 1 1 2 1
  • C 𝑎 𝑎 1 2 1 1
  • D ( 𝑎 𝑎 ) 1 1 1 2

Q2:

Find the matrix 𝐴 = 𝑎 𝑥 𝑦 , with an order of 3 × 3 , whose elements are given by the formula 𝑎 = 5 𝑥 + 4 𝑦 𝑥 𝑦 .

  • A 9 1 4 1 9 1 4 1 8 2 2 1 9 2 3 2 7
  • B 9 1 4 1 9 1 3 1 8 2 3 1 7 2 2 2 7
  • C 9 1 3 1 7 1 4 1 8 2 2 1 7 2 2 2 7
  • D 9 1 3 1 7 1 4 1 8 2 2 1 9 2 3 2 7

Q3:

Given that 𝐴 = 𝑎 𝑖 𝑗 where 𝑎 = 3 𝑖 + 5 𝑗 + 9 𝑖 𝑗 , find the matrix 𝐴 𝑇 .

  • A 2 3 2 0 1 7 2 8 2 5 2 3
  • B 2 2 2 5 2 8 1 7 2 0 2 3
  • C 1 7 2 2 2 0 2 5 2 3 2 8
  • D 1 7 2 0 2 3 2 2 2 5 2 8

Q4:

Which of the following is the matrix 𝐴 = 𝑎 𝑖 𝑗 , where 𝑖 = 1 , 2 and 𝑗 = 1 , 2 , 3 ?

  • A 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 1 1 2 1 3 1 1 2 2 2 3 2
  • B 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 1 1 1 2 2 1 2 2 3 1 3 2
  • C 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 1 1 2 1 1 2 2 2 1 3 2 3
  • D 𝑎 𝑎 𝑎 𝑎 𝑎 𝑎 1 1 1 2 1 3 2 1 2 2 2 3

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