Worksheet: Solving a System of Three Equations Using Matrices

In this worksheet, we will practice using matrices to solve systems of three linear equations.

Q1:

Solve 1 1 1 1 1 1 1 1 0 𝑥 𝑦 𝑧 = 9 1 1 6 using the inverse of a matrix.

  • A 𝑥 = 9 , 𝑦 = 1 1 , 𝑧 = 1 7
  • B 𝑥 = 1 0 , 𝑦 = 1 6 , 𝑧 = 1 7
  • C 𝑥 = 1 1 , 𝑦 = 9 , 𝑧 = 1 7
  • D 𝑥 = 1 6 , 𝑦 = 1 0 , 𝑧 = 1 7
  • E 𝑥 = 1 7 , 𝑦 = 1 0 , 𝑧 = 1 6

Q2:

Given that 1 1 1 2 0 0 8 4 0 𝑥 𝑦 𝑧 = 4 8 0 , find the values of 𝑥 , 𝑦 , and 𝑧 .

  • A 𝑥 = 1 6 , 𝑦 = 8 , 𝑧 = 4
  • B 𝑥 = 8 , 𝑦 = 4 , 𝑧 = 1 6
  • C 𝑥 = 1 6 , 𝑦 = 4 , 𝑧 = 8
  • D 𝑥 = 4 , 𝑦 = 8 , 𝑧 = 1 6

Q3:

Given that 1 6 6 0 2 4 2 4 7 𝑥 𝑦 𝑧 = 8 2 9 , find the values of 𝑥 , 𝑦 , and 𝑧 .

  • A 𝑥 = 3 , 𝑦 = 5 , 𝑧 = 4
  • B 𝑥 = 5 , 𝑦 = 4 , 𝑧 = 3
  • C 𝑥 = 3 , 𝑦 = 4 , 𝑧 = 5
  • D 𝑥 = 4 , 𝑦 = 5 , 𝑧 = 3

Q4:

Given that 9 3 0 4 3 5 8 7 8 𝑥 𝑦 𝑧 = 9 1 5 , find the values of 𝑥 , 𝑦 , and 𝑧 .

  • A 𝑥 = 2 , 𝑦 = 3 , 𝑧 = 0
  • B 𝑥 = 3 , 𝑦 = 0 , 𝑧 = 2
  • C 𝑥 = 2 , 𝑦 = 0 , 𝑧 = 3
  • D 𝑥 = 0 , 𝑦 = 3 , 𝑧 = 2

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.