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Lesson: LU Doolittle's Method

In this lesson, we will learn how to find the LU decomposition (factorization) of a matrix using Doolittle’s method.

Worksheet • 11 Questions

Q1:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q2:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q3:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D

Q4:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q5:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q6:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q7:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q8:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q9:

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

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q10:

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

  • A 𝑦 = 4 , π‘₯ = βˆ’ 3
  • B 𝑦 = 5 , π‘₯ = βˆ’ 4
  • C 𝑦 = 5 , π‘₯ = 6
  • D 𝑦 = βˆ’ 5 , π‘₯ = βˆ’ 6
  • E 𝑦 = βˆ’ 4 , π‘₯ = 3

Q11:

Consider the equations π‘₯ + 2 𝑦 + 𝑧 = 1 , 𝑦 + 3 𝑧 = 2 , and 2 π‘₯ + 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 = βˆ’ 1 6 , π‘₯ = 2 7
  • B 𝑧 = 1 , 𝑦 = βˆ’ 2 , π‘₯ = 6
  • C 𝑧 = 1 , 𝑦 = 2 , π‘₯ = 6
  • D 𝑧 = βˆ’ 6 , 𝑦 = βˆ’ 1 6 , π‘₯ = 2 7
  • E 𝑧 = 6 , 𝑦 = 1 6 , π‘₯ = 2 7
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