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

Q1:

Find an LU factoring of the matrix

Q2:

Q3:

Q4:

Q5:

Q6:

Q7:

Q8:

Q9:

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

Q10:

Find the LU factorization of the coefficient matrix, using Doolittleβs method, and use it to solve the system of equations π₯ + 2 π¦ = 5 and 2 π₯ + 3 π¦ = 6 .

Q11:

Consider the equations π₯ + 2 π¦ + π§ = 1 , π¦ + 3 π§ = 2 , and 2 π₯ + 3 π¦ = 6 . Use Doolittleβs method to find an LU factorization of the coefficient matrix of this system of equations, and hence solve the system.

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