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

In this lesson, we will learn how to check the number of solutions for a given homogeneous system of linear equations.

Sample Question Videos

  • 03:53

Worksheet: 7 Questions • 1 Video

Q1:

Determine the number of solutions to the system of equations − 6 𝑥 − 2 𝑦 + 9 𝑧 = − 4 , − 2 4 𝑥 − 8 𝑦 + 3 6 𝑧 = − 2 2 , − 1 2 𝑥 − 4 𝑦 + 1 8 𝑧 = − 1 0 .

Q2:

Determine the number of solutions to the following system: 4 − 8 0 1 3 0 1 1 0 − 1 4 1 7 𝑥 𝑦 𝑧 = 0 0 0 .

Q3:

Determine the number of solutions to the system of equations 4 𝑥 − 4 𝑦 = 0 , − 8 𝑥 − 2 𝑧 = 0 , 5 𝑦 − 7 𝑧 = 0 .

Q4:

Determine the number of solutions to the system of equations − 2 𝑥 + 2 𝑦 = 0 , 3 𝑥 − 3 𝑧 = 0 , 7 𝑦 + 4 𝑧 = 0 .

Q5:

Determine the number of solutions to the system of equations 9 𝑥 − 3 𝑦 + 8 𝑧 = 4 , 4 5 𝑥 − 1 5 𝑦 + 4 0 𝑧 = 2 0 , 1 8 𝑥 − 6 𝑦 + 1 6 𝑧 = 8 .

Q6:

Determine the number of solutions to the following system: − 1 4 − 1 3 0 7 0 − 2 1 0 3 2 0 𝑥 𝑦 𝑧 = 0 0 0 .

Q7:

Determine the number of solutions to the following system: − 5 0 2 3 − 1 5 0 6 9 − 1 0 0 4 6 𝑥 𝑦 𝑧 = 1 2 3 6 1 9 .

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