Worksheet: LDU and PLU Decomposition

In this worksheet, we will practice finding the LDU and PLU decompositions of a matrix.

Q1:

Find a PLU factoring of the matrix 121122211.

  • 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 2 1 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 1 2 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

Q2:

Find a PLU factoring of the matrix 121122241321.

  • 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 2 1 2 1 0 4 3 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 1 1 2 1 0 4 2 0 0 1 0 0 0

Q3:

Find a PLU factoring of the matrix 121212424112132.

  • 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

Q4:

Which of the following is a correct PLU factorization of the matrix 𝐴=01031002121011421030.

  • A L U P = 1 0 0 0 2 1 0 0 0 1 1 0 0 0 1 1 , = 1 0 0 0 0 0 1 2 1 8 0 0 2 2 7 0 0 0 1 5 , = 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0
  • B L U P = 1 0 0 0 2 1 0 0 0 1 1 0 0 0 1 1 , = 1 0 1 1 4 0 1 2 1 8 0 0 2 2 7 0 0 0 1 5 , = 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0
  • C L U P = 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 , = 1 0 1 1 4 0 1 2 1 8 0 0 2 2 7 0 0 0 1 5 , = 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0
  • D L U P = 1 0 0 0 2 1 0 0 0 1 1 0 0 0 1 1 , = 1 0 1 1 4 0 1 2 1 8 0 0 2 2 7 0 0 0 1 5 , = 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0

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