Suppose the LU de 1 00 position is already computed as 4 1 -1 02 1 , then 3 5 1 0 0 3 (for the row vectors, input numbers separated only by one comma). A = -21 0 \ the 1st row of A is [ the 2nd row of A is [ X 6 X 2 X 12 the 3rd row of A is [ To solve Ax = b, you need to utilize the LU factors and solve LUx=b in two steps: Step 1: Solve Ly = b for y; Step 2: Solve Ux = y for a. Now carry out the above two steps to solve Axb for the b given below 1 -2 3 0 0 4 1 16 5 1 00 10 02 21 JB- X2 3 = -6 13 -16_
Suppose the LU de 1 00 position is already computed as 4 1 -1 02 1 , then 3 5 1 0 0 3 (for the row vectors, input numbers separated only by one comma). A = -21 0 \ the 1st row of A is [ the 2nd row of A is [ X 6 X 2 X 12 the 3rd row of A is [ To solve Ax = b, you need to utilize the LU factors and solve LUx=b in two steps: Step 1: Solve Ly = b for y; Step 2: Solve Ux = y for a. Now carry out the above two steps to solve Axb for the b given below 1 -2 3 0 0 4 1 16 5 1 00 10 02 21 JB- X2 3 = -6 13 -16_
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
Transcribed Image Text:Step 1: Solve the lower triangular equation forwardly:
y1 =
-6
x 7
x 13
Y/2 =
Step 2: Solve the upper triangular equation backwardly:
X2
Y3 =
X 5
X -16
x3 =
x 2
1 00 Y₁
-2
1 0 Y/2
3
5 1
1/3
T (input numbers separated only by a comma)
=
4 1
02
00 3
-11 x1
1 X2 =
Iz
-6
13
-16
X1
If you are asked to solve Ax = -3 * b for the same A, bas given above. Then, without doing any more equation solving, you know that the new solution should be the vector [
X 6,4,2,0
Y₁
Y/2
3/3
Transcribed Image Text:Suppose the LU decomposition is already computed as
4 1 -
1 0 0
-2 10
02
3
5 1
0 0 3
(for the row vectors, input numbers separated only by one comma)
A =
the 1st row of A is [
the 2nd row of A is [
X 6
X 2
× 12
1 , then
the 3rd row of A is [
To solve Az = b, you need to utilize the LU factors and solve LU = b in two steps:
Step 1: Solve Ly = b for y;
Step 2: Solve Ux = y for x.
Now carry out the above two steps to solve Ax = b for the b given below
01
-2
1
0
3 5 1
4
1
0 2
-17
1
00 3
x1
X2
13
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