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Worksheet: Systems of Linear Equations in Matrix Notation

In this worksheet, we will practice expressing a system of linear equations as a matrix equation and writing a set of simultaneous equations from a matrix equation.

Q1:

Express the following set of simultaneous equations as a matrix equation:

  • A
  • B
  • C
  • D
  • E

Q2:

Express the set of simultaneous equations as a matrix equation.

  • A
  • B
  • C
  • D
  • E

Q3:

Write down the set of simultaneous equations that could be solved using the matrix equation 2 2 4 − 1 − 1 − 1 2 5 6 𝑝 𝑞 𝑟 = 4 1 4 1 0 .

  • A 2 𝑝 + 4 𝑞 + 2 𝑟 = 4 , − 𝑝 − 𝑞 − 𝑟 = 1 4 , 2 𝑝 + 6 𝑞 + 5 𝑟 = 1 0
  • B 2 𝑝 − 𝑞 + 2 𝑟 = 4 , 2 𝑝 − 𝑞 + 5 𝑟 = 1 4 , 4 𝑝 − 𝑞 + 6 𝑟 = 1 0
  • C 2 𝑝 − 𝑞 + 2 𝑟 = 1 4 , 2 𝑝 − 𝑞 + 5 𝑟 = 1 0 , 4 𝑝 − 𝑞 + 6 𝑟 = 4
  • D 2 𝑝 + 2 𝑞 + 4 𝑟 = 4 , − 𝑝 − 𝑞 − 𝑟 = 1 4 , 2 𝑝 + 5 𝑞 + 6 𝑟 = 1 0
  • E 2 𝑝 + 2 𝑞 + 4 𝑟 = 1 4 , − 𝑝 − 𝑞 − 𝑟 = 1 0 , 2 𝑝 + 5 𝑞 + 6 𝑟 = 4

Q4:

Find the matrix 𝐴 such that

  • A ⎡ ⎢ ⎢ ⎣ 1 3 2 0 2 1 0 0 6 0 0 0 1 3 1 0 ⎤ ⎥ ⎥ ⎦
  • B ⎡ ⎢ ⎢ ⎣ 1 1 0 1 3 0 0 3 2 2 6 0 0 0 0 1 ⎤ ⎥ ⎥ ⎦
  • C ⎡ ⎢ ⎢ ⎣ 1 2 0 1 3 1 6 3 2 0 0 1 0 0 0 0 ⎤ ⎥ ⎥ ⎦
  • D ⎡ ⎢ ⎢ ⎣ 1 3 2 0 1 0 2 0 0 0 6 0 1 3 0 1 ⎤ ⎥ ⎥ ⎦
  • E ⎡ ⎢ ⎢ ⎣ 1 2 6 1 3 1 0 3 2 0 0 1 0 0 0 0 ⎤ ⎥ ⎥ ⎦

Q5:

Express the simultaneous equations as a matrix equation.

  • A ⎡ ⎢ ⎢ ⎣ 1 3 3 4 − 2 3 1 4 ⎤ ⎥ ⎥ ⎦ 𝑥 𝑦 = ⎡ ⎢ ⎢ ⎣ 7 4 5 3 ⎤ ⎥ ⎥ ⎦
  • B ⎡ ⎢ ⎢ ⎣ 1 3 − 2 3 3 4 1 4 ⎤ ⎥ ⎥ ⎦ 𝑥 𝑦 = ⎡ ⎢ ⎢ ⎣ 5 3 7 4 ⎤ ⎥ ⎥ ⎦
  • C ⎡ ⎢ ⎢ ⎣ 1 3 1 4 3 4 − 2 3 ⎤ ⎥ ⎥ ⎦ 𝑥 𝑦 = ⎡ ⎢ ⎢ ⎣ 7 4 5 3 ⎤ ⎥ ⎥ ⎦
  • D ⎡ ⎢ ⎢ ⎣ 1 3 − 2 3 1 4 3 4 ⎤ ⎥ ⎥ ⎦ 𝑥 𝑦 = ⎡ ⎢ ⎢ ⎣ 5 3 7 4 ⎤ ⎥ ⎥ ⎦
  • E ⎡ ⎢ ⎢ ⎣ − 2 3 1 3 3 4 1 4 ⎤ ⎥ ⎥ ⎦ 𝑥 𝑦 = ⎡ ⎢ ⎢ ⎣ 5 3 7 4 ⎤ ⎥ ⎥ ⎦

Q6:

Write in the form where 𝐴 is a matrix.

  • A ⎡ ⎢ ⎢ ⎣ 1 1 1 0 2 1 1 0 1 − 1 0 0 3 1 0 0 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • B ⎡ ⎢ ⎢ ⎣ 1 1 − 1 1 1 1 0 0 1 2 1 0 0 0 0 3 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • C ⎡ ⎢ ⎢ ⎣ 1 2 1 3 1 1 − 1 1 1 1 0 0 0 0 0 0 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • D ⎡ ⎢ ⎢ ⎣ 1 1 1 0 1 1 2 0 − 1 0 1 0 1 0 0 3 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • E ⎡ ⎢ ⎢ ⎣ 1 2 1 3 1 1 − 1 1 1 1 0 1 0 0 0 1 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4

Q7:

Which of the following shows the set of simultaneous equations that could be solved using the matrix equation

  • A
  • B
  • C
  • D
  • E

Q8:

Which of the following shows the set of simultaneous equations that could be solved using the given matrix equation?

  • A
  • B
  • C
  • D
  • E

Q9:

Express the simultaneous equations as a matrix equation.

  • A 7 5 − 3 − 2 𝑥 𝑦 = 1 1 5
  • B 7 − 3 5 − 2 𝑥 𝑦 = 1 1 5
  • C 7 5 − 3 − 2 𝑥 𝑦 = 5 1 1
  • D 7 − 3 5 − 2 𝑥 𝑦 = 5 1 1
  • E − 3 7 − 2 5 𝑥 𝑦 = 5 1 1

Q10:

Write in the form where 𝐴 is a matrix.

  • A ⎡ ⎢ ⎢ ⎣ 1 1 0 1 − 1 0 0 3 2 2 3 0 0 0 0 3 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • B ⎡ ⎢ ⎢ ⎣ 1 − 1 2 0 2 1 0 0 3 0 0 0 3 3 1 0 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • C ⎡ ⎢ ⎢ ⎣ 1 2 3 3 − 1 1 0 3 2 0 0 1 0 0 0 0 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • D ⎡ ⎢ ⎢ ⎣ 1 − 1 2 0 1 0 2 0 0 0 3 0 1 3 0 3 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4
  • E ⎡ ⎢ ⎢ ⎣ 1 1 2 0 1 0 2 0 0 0 3 0 1 3 0 3 ⎤ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎣ 𝑥 𝑥 𝑥 𝑥 ⎤ ⎥ ⎥ ⎦ 1 2 3 4

Q11:

Write down the set of simultaneous equations that could be solved using the given matrix equation.

  • A
  • B
  • C
  • D
  • E

Q12:

Express the following system of equations in matrix form.

  • A
  • B
  • C
  • D

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