Worksheet: LU Decomposition: Row Operations

In this worksheet, we will practice finding the LU decomposition (factorization) of a matrix and using the LU decomposition to simplify the solution of a system of linear equations.

Q1:

Find an LU factoring of the matrix 123213215013.

  • A101100110513220011012417
  • B10110011051312001101247
  • C100101510112230111002417
  • D100110510112320011012417
  • E100110510112320111002417

Q2:

Find an LU factoring of the matrix 321986622327.

  • A1000310021101221321023001000
  • B1000310021101221321023001000
  • C1000310021101221221033001000
  • D1000310021101221321023001000
  • E1000310021101221321023001000

Q3:

Find an LU factoring of the matrix 13113039041216.

  • A1000110030104041131001003000
  • B1000110030104041131001003000
  • C1000110030104041131001003000
  • D1000110030104041131001003000
  • E1000110030104041133002003000

Q4:

Find an LU factoring of the matrix 12502511336151.

  • A100201301125001130001
  • B100201301125001130001
  • C100210301125001130001
  • D100201301122001140001
  • E100201301125000130010

Q5:

Find the LU decomposition for the matrix 𝐴=102411323.

  • A1004102311020190028=102411323
  • B10021032212010130092=102411323
  • C1004103211020190021=102411323
  • D1004103211020190021=102411323
  • E100410321102017008=102411323

Q6:

Find the LU decomposition for the matrix 𝐴=1011020212203211.

  • A100001001110314110110202001300018=1011020212203211
  • B100001001110314110110202001300018=1011020212203211
  • C100001001110314110110202001300018=1011020212203211
  • D100001001110314110110202001300018=1011020212203211
  • E100011001110314110110212001300018=1011020212203211

Q7:

Find the LU decomposition for the matrix 𝐴=183270301.

  • A10021038311830960024=183270301
  • B100230388183032001=183270301
  • C1002103831183096008=183270301
  • D10011032411830130064=183270301
  • E1002103831183096008=183270301

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