Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Homogeneous Systems of Linear Equations

Q1:

Consider the matrix

Find the matrix with the smallest positive integer entries, 𝑋 ,such that

  • A 𝑋 =  5 3 
  • B 𝑋 =  3 5 
  • C 𝑋 =  3 5 
  • D 𝑋 =  3 5 
  • E 𝑋 =  5 3 

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

  • A 𝑇 =  4 5 
  • B 𝑇 =  1 3 
  • C 𝑇 =  5 4 
  • D 𝑇 =  4 3 
  • E 𝑇 =  3 1 

Q2:

If 𝑏 β‰  0 and 𝐴 is an invertible 𝑛 Γ— 𝑛 matrix, can the solution set of ⃑ 𝐴 π‘₯ = ⃑ 𝑏 be a plane through the origin?

  • Ano
  • Byes

Q3:

Which of the following systems of equations is homogeneous?

  • A 5 π‘₯ βˆ’ 7 𝑦 = 4 , βˆ’ 2 π‘₯ βˆ’ 9 𝑦 = 0
  • B βˆ’ 6 π‘₯ + 2 𝑦 = 0 , 7 π‘₯ βˆ’ 8 𝑦 = 1 5
  • C 5 π‘₯ βˆ’ 7 𝑦 = 4 , βˆ’ 2 π‘₯ βˆ’ 9 𝑦 = 1 5
  • D βˆ’ 6 π‘₯ + 2 𝑦 = 0 , 7 π‘₯ βˆ’ 8 𝑦 = 0