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

**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
- E

**Q4: **

Find an LU factoring of the matrix

- A
- B
- C
- D

**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: **

Find the LU factorization of the coefficient matrix, using Doolittleβs method, and use it to solve the system of equations and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q10: **

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

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q11: **

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.

- A ,
- B ,
- C ,
- D ,
- E ,