Worksheet: Number of Solutions to a Homogeneous System of Linear Equations

In this worksheet, we will practice checking the number of solutions for a given homogeneous system of linear equations.

Q1:

Determine the number of solutions to the system of equations

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

Q2:

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 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .

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 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is 𝑥 = 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 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .

Q5:

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 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .

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 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .

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 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .
  • DThe only solution is 𝑥 = 0 , 𝑦 = 0 , 𝑧 = 0 .

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