L, U, and b are in the other attached image for the problem. 0 060 0 U? The0 0What would the answer be for Ax = b if A = L5matrices L, U and b are as in the above.1/3 [ 1-1 1-1 11-1L =and U = |01-11= b1

Given that A=L160001500013U, Where L=100−1100−11 and U=1−1001−1001 We have solve the equation Ax=b…

Answered: 0 0 What would the answer be for Ax = b…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

L, U, and b are in the other attached image for the problem.

0 0
6
0 0 U? The
0 0
What would the answer be for Ax = b if A = L
5
matrices L, U and b are as in the above.
1/3

[ 1
-1 1
-1 1
1
-1
L =
and U = |0
1
-1
1
= b
1

Expert Solution

Step 1

Given that $A = L [\begin{matrix} \frac{1}{6} & 0 & 0 \\ 0 & \frac{1}{5} & 0 \\ 0 & 0 & \frac{1}{3} \end{matrix}] U$ , Where $L = [\begin{matrix} 1 & 0 & 0 \\ - 1 & 1 & 0 \\ 0 & - 1 & 1 \end{matrix}]$ and $U = [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}]$

We have solve the equation $A x = b$ where, $b = [\begin{matrix} 1 \\ 1 \\ 1 \end{matrix}]$

Substitute $L = [\begin{matrix} 1 & 0 & 0 \\ - 1 & 1 & 0 \\ 0 & - 1 & 1 \end{matrix}]$ and $U = [\begin{matrix} 1 & - 1 & 0 \\ 0 & 1 & - 1 \\ 0 & 0 & 1 \end{matrix}]$ in $A = L [\begin{matrix} \frac{1}{6} & 0 & 0 \\ 0 & \frac{1}{5} & 0 \\ 0 & 0 & \frac{1}{3} \end{matrix}] U$

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