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Worksheet: Homogeneous Systems of Linear Equations

Q1:

Determine the number of solutions to the system of equations

  • AThere are no solutions.
  • BThere are infinitely many solutions.
  • CThere are finitely many solutions, not including π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .

Q2:

Determine the number of solutions to the system of equations

  • AThere are infinitely many solutions.
  • BThe only solution is π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • CThere are finitely many solutions, not including π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThere are no solutions.

Q3:

Determine the number of solutions to the system of equations

  • AThere are no solutions.
  • BThere are infinitely many solutions.
  • CThere are finitely many solutions, not including π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .

Q4:

Determine the number of solutions to the system of equations

  • AThere are no solutions.
  • BThere are infinitely many solutions.
  • CThere are finitely many solutions, not including π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is π‘₯ = 0 , 𝑦 = 0 , 𝑧 = 0 .

Q5:

Determine the number of solutions to the following system.

  • AThere are no solutions.
  • BThere are infinitely many solutions.
  • CThere are finitely many solutions, not including .
  • DThe only solution is .

Q6:

Determine the number of solutions to the following system.

  • AThere are no solutions.
  • BThere are infinitely many solutions.
  • CThere are finitely many solutions, not including .
  • DThe only solution is .

Q7:

Determine the number of solutions to the following system.

  • AThere are no solutions.
  • BThere are infinitely many solutions.
  • CThere are finitely many solutions, not including .
  • DThe only solution is .