Worksheet: LU Doolittle's Method

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

  • A
  • B
  • C
  • D
  • E

Q2:

Find an LU factoring of the matrix

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  • B
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  • D
  • E

Q3:

Find an LU factoring of the matrix

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  • B
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  • D
  • E

Q4:

Find an LU factoring of the matrix

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  • B
  • C
  • D

Q5:

Find an LU factoring of the matrix

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  • 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

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  • B
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  • E

Q8:

Find an LU factoring of the matrix

  • A
  • B
  • C
  • D
  • E

Q9:

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

Q10:

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 = 1 6 , π‘₯ = 2 7
  • B 𝑧 = 1 , 𝑦 = 2 , π‘₯ = 6
  • C 𝑧 = βˆ’ 6 , 𝑦 = βˆ’ 1 6 , π‘₯ = 2 7
  • D 𝑧 = 6 , 𝑦 = βˆ’ 1 6 , π‘₯ = 2 7
  • E 𝑧 = 1 , 𝑦 = βˆ’ 2 , π‘₯ = 6

Q11:

Consider the following system of equations: π‘₯ + 2 𝑦 + 3 𝑧 = 5 , 2 π‘₯ + 3 𝑦 + 𝑧 = 6 , 3 π‘₯ + 5 𝑦 + 4 𝑧 = 1 1 . Use Doolittle’s method to find an LU factorisation of the coefficient matrix of this system of equations, and hence solve the system.

  • A ο€Ώ π‘₯ 𝑦 𝑧  =  3 βˆ’ 7 𝑑 4 βˆ’ 5 𝑑 𝑑  , 𝑑 ∈ ℝ
  • B ο€Ώ π‘₯ 𝑦 𝑧  =  7 𝑑 βˆ’ 3 5 𝑑 βˆ’ 4 𝑑  , 𝑑 ∈ ℝ
  • C ο€Ώ π‘₯ 𝑦 𝑧  =  3 βˆ’ 7 𝑑 5 βˆ’ 4 𝑑 𝑑  , 𝑑 ∈ ℝ
  • D ο€Ώ π‘₯ 𝑦 𝑧  =  7 𝑑 βˆ’ 3 4 βˆ’ 5 𝑑 𝑑  , 𝑑 ∈ ℝ
  • E ο€Ώ π‘₯ 𝑦 𝑧  =  3 βˆ’ 5 𝑑 5 βˆ’ 7 𝑑 𝑑  , 𝑑 ∈ ℝ

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