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Worksheet: PLU Decomposition

Q1:

Find a PLU factoring of the matrix

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

Q2:

Find a PLU factoring of the matrix

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

Q3:

Find a PLU factoring of the matrix

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