Lesson Worksheet: LU Decomposition: Doolittle’s Method Mathematics

In this worksheet, we will practice finding the LU decomposition (factorization) of a matrix using Doolittle’s method.

Q1:

Find an LU factoring of the matrix 134331010101625.

  • A100310131134301210001
  • B100310131134301210001
  • C100310131134301210001
  • D100310131134301210001
  • E100310131134301210001

Q2:

Find an LU factoring of the matrix 1311310812533.

  • A100310211131101520001
  • B100310211131101520001
  • C100310211131101520001
  • D100310211131101520001
  • E100310211131101520001

Q3:

Find an LU factoring of the matrix 113112432373.

  • A100110211113101120001
  • B100110211113101120001
  • C100110211113101120001
  • D100110211113101120001

Q4:

Find an LU factoring of the matrix 120213123.

  • A100220101120025003
  • B100210101120033003
  • C100210101120033003
  • D100210101120033003
  • E100120101120033003

Q5:

Consider the following system of equations: 𝑥+2𝑦+3𝑧=5,2𝑥+3𝑦+𝑧=6,3𝑥+5𝑦+4𝑧=11. Use Doolittle’s method to find an LU factorization of the coefficient matrix of this system of equations, and hence solve the system.

  • A𝑥𝑦𝑧=37𝑡45𝑡𝑡, 𝑡
  • B𝑥𝑦𝑧=37𝑡54𝑡𝑡, 𝑡
  • C𝑥𝑦𝑧=35𝑡57𝑡𝑡, 𝑡
  • D𝑥𝑦𝑧=7𝑡345𝑡𝑡, 𝑡
  • E𝑥𝑦𝑧=7𝑡35𝑡4𝑡, 𝑡

Q6:

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

  • A𝑦=5, 𝑥=6
  • B𝑦=4, 𝑥=3
  • C𝑦=5, 𝑥=4
  • D𝑦=5, 𝑥=6
  • E𝑦=4, 𝑥=3

Q7:

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

  • A𝑧=1, 𝑦=2, 𝑥=6
  • B𝑧=6, 𝑦=16, 𝑥=27
  • C𝑧=6, 𝑦=16, 𝑥=27
  • D𝑧=6, 𝑦=16, 𝑥=27
  • E𝑧=1, 𝑦=2, 𝑥=6

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