Worksheet: Homogeneous Systems of Linear Equations

In this worksheet, we will practice finding the solution of a homogeneous system of linear equations and expressing the general solution in case of an infinite number of solutions.

Q1:

Which of the following systems of equations is homogeneous?

  • A 6 𝑥 + 2 𝑦 = 0 , 7 𝑥 8 𝑦 = 1 5
  • B 5 𝑥 7 𝑦 = 4 , 2 𝑥 9 𝑦 = 0
  • C 5 𝑥 7 𝑦 = 4 , 2 𝑥 9 𝑦 = 1 5
  • D 6 𝑥 + 2 𝑦 = 0 , 7 𝑥 8 𝑦 = 0

Q2:

Find the value of 𝑘 that would make the equations 4𝑥+9𝑦+5𝑧=0, 16𝑥+36𝑦+𝑘𝑧=0, and 9𝑥8𝑦3𝑧=0 have a solution other than zero.

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