Worksheet: Homogeneous Systems of Linear Equations

In this worksheet, we will practice solving a Homogeneous system of Linear Equations using Elementary row operations.

Q1:

Consider the matrix

Find the matrix with the smallest positive integer entries such that

  • A
  • B
  • C
  • D
  • E

Find the matrix with the smallest non-zero positive integer entries, , such that

  • A
  • B
  • C
  • D
  • E

Q2:

If 𝑏 0 and 𝐴 is an invertible 𝑛 × 𝑛 matrix, can the solution set of 𝐴 𝑥 = 𝑏 be a plane through the origin?

  • ANo
  • BYes

Q3:

Which of the following systems of equations is homogeneous?

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

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