- #1
Master1022
- 611
- 117
- Homework Statement
- Find the LU Decomposition of the matrix below
- Relevant Equations
- M = LU
Here is the initial matrix M:
[tex] M = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ 0 & 8 & -17 \end{bmatrix} [/tex]
I have used the shortcut method outlined in this youtube video: LU Decomposition Shortcut Method.
Here are the row reductions that I went through in order to get my U matrix:
1. [itex] R_3 - 8 R_1 [/itex]
[tex] = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ -24 & 0 & -65 \end{bmatrix} [/tex]
2. [itex] R_3 - 4 R_2 [/itex]
[tex] = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ 0 & 0 & -1 \end{bmatrix} [/tex]
3. [itex] R_2 + 2 R_1 [/itex]
[tex] U = \begin{bmatrix} 3 & 1 & 6 \\ 0 & 2 & -4 \\ 0 & 0 & -1 \end{bmatrix} [/tex]
This yields the correct U matrix, however, I get a slightly different L matrix to the answer. My L matrix is:
[tex] L = \begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 4 & 8 & 1 \end{bmatrix} [/tex]
In the answer, the final row reads 0, 4, 1.
Why would this be the case?
Any help is greatly appreciated.
[tex] M = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ 0 & 8 & -17 \end{bmatrix} [/tex]
I have used the shortcut method outlined in this youtube video: LU Decomposition Shortcut Method.
Here are the row reductions that I went through in order to get my U matrix:
1. [itex] R_3 - 8 R_1 [/itex]
[tex] = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ -24 & 0 & -65 \end{bmatrix} [/tex]
2. [itex] R_3 - 4 R_2 [/itex]
[tex] = \begin{bmatrix} 3 & 1 & 6 \\ -6 & 0 & -16 \\ 0 & 0 & -1 \end{bmatrix} [/tex]
3. [itex] R_2 + 2 R_1 [/itex]
[tex] U = \begin{bmatrix} 3 & 1 & 6 \\ 0 & 2 & -4 \\ 0 & 0 & -1 \end{bmatrix} [/tex]
This yields the correct U matrix, however, I get a slightly different L matrix to the answer. My L matrix is:
[tex] L = \begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 0 \\ 4 & 8 & 1 \end{bmatrix} [/tex]
In the answer, the final row reads 0, 4, 1.
Why would this be the case?
Any help is greatly appreciated.