2. Find the LU factorizations of and 20 0 -6 3 4 9 5 2 -13 -3 16 17 2 4 3 2 13 9 -65 4
2. Find the LU factorizations of and 20 0 -6 3 4 9 5 2 -13 -3 16 17 2 4 3 2 13 9 -65 4
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![2. Find the LU factorizations of
\[
\begin{bmatrix}
2 & 0 & 5 & 2 \\
-6 & 3 & -13 & -3 \\
4 & 9 & 16 & 17
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
2 & 3 & 2 \\
4 & 13 & 9 \\
-6 & 5 & 4
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F327c4acc-aab0-4600-9811-c42079067cf3%2F60a2c17b-e55e-4988-bae2-b065a7f6a4c7%2Fo8z2nzj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Find the LU factorizations of
\[
\begin{bmatrix}
2 & 0 & 5 & 2 \\
-6 & 3 & -13 & -3 \\
4 & 9 & 16 & 17
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
2 & 3 & 2 \\
4 & 13 & 9 \\
-6 & 5 & 4
\end{bmatrix}
\]
Expert Solution

Step 1
First, we have
Let the lower triangular matrix be
Consider
Apply (which gives )
Apply (which gives )
Apply (which gives )
So, the upper triangular matrix is and the lower triangular matrix is
So, decomposition of is :
Step by step
Solved in 2 steps

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