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Worksheet: LU Doolittle's Method

Q1:

Find an LU factoring of the matrix

  • A 1 0 0 3 1 0 1 3 1 1 3 4 3 0 1 2 1 0 0 0 1
  • B 1 0 0 3 1 0 1 3 1 1 3 4 3 0 1 2 1 0 0 0 1
  • C 1 0 0 3 1 0 1 3 1 1 3 4 3 0 1 2 1 0 0 0 1
  • D 1 0 0 3 1 0 1 3 1 1 3 4 3 0 1 2 1 0 0 0 1
  • E 1 0 0 3 1 0 1 3 1 1 3 4 3 0 1 2 1 0 0 0 1

Q2:

Find an LU factoring of the matrix

  • A 1 0 0 3 1 0 2 1 1 1 3 1 1 0 1 5 2 0 0 0 1
  • B 1 0 0 3 1 0 2 1 1 1 3 1 1 0 1 5 2 0 0 0 1
  • C 1 0 0 3 1 0 2 1 1 1 3 1 1 0 1 5 2 0 0 0 1
  • D 1 0 0 3 1 0 2 1 1 1 3 1 1 0 1 5 2 0 0 0 1
  • E 1 0 0 3 1 0 2 1 1 1 3 1 1 0 1 5 2 0 0 0 1

Q3:

Find an LU factoring of the matrix

  • A 1 0 0 1 1 0 2 1 1 1 1 3 1 0 1 1 2 0 0 0 1
  • B 1 0 0 1 1 0 2 1 1 1 1 3 1 0 1 1 2 0 0 0 1
  • C 1 0 0 1 1 0 2 1 1 1 1 3 1 0 1 1 2 0 0 0 1
  • D 1 0 0 1 1 0 2 1 1 1 1 3 1 0 1 1 2 0 0 0 1

Q4:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q5:

Find an LU factoring of the matrix

  • A 1 0 0 0 3 1 0 0 2 1 1 0 1 2 2 1 3 2 1 0 2 3 0 0 1 0 0 0
  • B 1 0 0 0 3 1 0 0 2 1 1 0 1 2 2 1 3 2 1 0 2 3 0 0 1 0 0 0
  • C 1 0 0 0 3 1 0 0 2 1 1 0 1 2 2 1 3 2 1 0 2 3 0 0 1 0 0 0
  • D 1 0 0 0 3 1 0 0 2 1 1 0 1 2 2 1 3 2 1 0 2 3 0 0 1 0 0 0
  • E 1 0 0 0 3 1 0 0 2 1 1 0 1 2 2 1 2 2 1 0 3 3 0 0 1 0 0 0

Q6:

Find an LU factoring of the matrix

  • A 1 0 0 0 1 1 0 0 3 0 1 0 4 0 4 1 1 3 1 0 0 1 0 0 3 0 0 0
  • B 1 0 0 0 1 1 0 0 3 0 1 0 4 0 4 1 1 3 1 0 0 1 0 0 3 0 0 0
  • C 1 0 0 0 1 1 0 0 3 0 1 0 4 0 4 1 1 3 1 0 0 1 0 0 3 0 0 0
  • D 1 0 0 0 1 1 0 0 3 0 1 0 4 0 4 1 1 3 1 0 0 1 0 0 3 0 0 0
  • E 1 0 0 0 1 1 0 0 3 0 1 0 4 0 4 1 1 3 3 0 0 2 0 0 3 0 0 0

Q7:

Find an LU factoring of the matrix

  • A 1 0 0 2 0 1 3 0 1 1 2 5 0 0 0 1 3 0 0 1 0
  • B 1 0 0 2 0 1 3 0 1 1 2 5 0 0 1 1 3 0 0 0 1
  • C 1 0 0 2 0 1 3 0 1 1 2 5 0 0 1 1 3 0 0 0 1
  • D 1 0 0 2 1 0 3 0 1 1 2 5 0 0 1 1 3 0 0 0 1
  • E 1 0 0 2 0 1 3 0 1 1 2 2 0 0 1 1 4 0 0 0 1

Q8:

Find an LU factoring of the matrix

  • A 1 0 0 2 1 0 1 0 1 1 2 0 0 3 3 0 0 3
  • B 1 0 0 1 2 0 1 0 1 1 2 0 0 3 3 0 0 3
  • C 1 0 0 2 1 0 1 0 1 1 2 0 0 3 3 0 0 3
  • D 1 0 0 2 1 0 1 0 1 1 2 0 0 3 3 0 0 3
  • E 1 0 0 2 2 0 1 0 1 1 2 0 0 2 5 0 0 3

Q9:

Consider the following system of equations: Use Doolittle’s method to find an LU factorization of the coefficient matrix of this system of equations, and hence solve the system.

  • A 𝑥 𝑦 𝑧 = 3 7 𝑡 4 5 𝑡 𝑡 , 𝑡
  • B 𝑥 𝑦 𝑧 = 7 𝑡 3 5 𝑡 4 𝑡 , 𝑡
  • C 𝑥 𝑦 𝑧 = 3 7 𝑡 5 4 𝑡 𝑡 , 𝑡
  • D 𝑥 𝑦 𝑧 = 7 𝑡 3 4 5 𝑡 𝑡 , 𝑡
  • E 𝑥 𝑦 𝑧 = 3 5 𝑡 5 7 𝑡 𝑡 , 𝑡

Q10:

Find the LU factorization of the coefficient matrix, using Doolittle’s method, and use it to solve the system of equations 𝑥 + 2 𝑦 = 5 and 2 𝑥 + 3 𝑦 = 6 .

  • A 𝑦 = 4 , 𝑥 = 3
  • B 𝑦 = 5 , 𝑥 = 6
  • C 𝑦 = 5 , 𝑥 = 6
  • D 𝑦 = 4 , 𝑥 = 3
  • E 𝑦 = 5 , 𝑥 = 4

Q11:

Consider the equations 𝑥 + 2 𝑦 + 𝑧 = 1 , 𝑦 + 3 𝑧 = 2 , and 2 𝑥 + 3 𝑦 = 6 . Use Doolittle’s method to find an LU factorization of the coefficient matrix of this system of equations, and hence solve the system.

  • A 𝑧 = 6 , 𝑦 = 1 6 , 𝑥 = 2 7
  • B 𝑧 = 1 , 𝑦 = 2 , 𝑥 = 6
  • C 𝑧 = 6 , 𝑦 = 1 6 , 𝑥 = 2 7
  • D 𝑧 = 6 , 𝑦 = 1 6 , 𝑥 = 2 7
  • E 𝑧 = 1 , 𝑦 = 2 , 𝑥 = 6