Utilize the following linear system of equations for this activity. x₁ + 2x₂ + 3x₂ =9 3x₁ - x₂ = 3 2x₁ - x₂ + x₁ = 8 Note: Not all matrices have an LU decomposition. However, if the LU decomposition of a matrix doesn't exist, the rows of the matrix can always be permuted to yield a matrix that does have an LU decomposition. Consider the system of equations Ax=b where A does not have an LU decomposition. Let P be a permutation matrix (a matrix with a single 1 in each row and column). The permuted system of equations PAX = Pb still has the same solution, just the order in which the equations are written down is now different. For the correct permutation matrix, the matrix PA will have an LU decomposition. For more information, please see the MATLAB documentation for LU matrix factorization Script 1 XI need help with all of this, I feel I'm not doing this right. Save *Create the coefficient matrix A and and the column matrix b of constants. A [1 2 3; 3 -1; 2-11] 6b - [9; 3; 8] Reset MATLAB Documentation Use the lu() command to find the LU decomposition of A, storing the lower and upper matrices Xin L and U, respectively. 10 [L, U] - lu(A) 11 12 XSolve the system of linear equations Ax-b using the LU decomposition. Store the intermediary 13 %solution in y. Store the solution for x in x1. 14 y L\b 15 x1- U\b 16 %Check that the solution x1 matches that found by directly using the backslash operator to solve 17 %the system Ax-b. Use the backslash operator to solve Ax-b in one step, storing the solution in x2. 18 x2- Uly 19
Utilize the following linear system of equations for this activity. x₁ + 2x₂ + 3x₂ =9 3x₁ - x₂ = 3 2x₁ - x₂ + x₁ = 8 Note: Not all matrices have an LU decomposition. However, if the LU decomposition of a matrix doesn't exist, the rows of the matrix can always be permuted to yield a matrix that does have an LU decomposition. Consider the system of equations Ax=b where A does not have an LU decomposition. Let P be a permutation matrix (a matrix with a single 1 in each row and column). The permuted system of equations PAX = Pb still has the same solution, just the order in which the equations are written down is now different. For the correct permutation matrix, the matrix PA will have an LU decomposition. For more information, please see the MATLAB documentation for LU matrix factorization Script 1 XI need help with all of this, I feel I'm not doing this right. Save *Create the coefficient matrix A and and the column matrix b of constants. A [1 2 3; 3 -1; 2-11] 6b - [9; 3; 8] Reset MATLAB Documentation Use the lu() command to find the LU decomposition of A, storing the lower and upper matrices Xin L and U, respectively. 10 [L, U] - lu(A) 11 12 XSolve the system of linear equations Ax-b using the LU decomposition. Store the intermediary 13 %solution in y. Store the solution for x in x1. 14 y L\b 15 x1- U\b 16 %Check that the solution x1 matches that found by directly using the backslash operator to solve 17 %the system Ax-b. Use the backslash operator to solve Ax-b in one step, storing the solution in x2. 18 x2- Uly 19
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I need help with this activity, I feel like I'm not doing it right. In the activity you must use the system of linear equations to complete the tasks described in green.
![←
b
D2L
zy
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https://learn.zybooks.com/zybook/MAT-350-J6466-OL-TRAD-UG.22EW6/chapter/2/section/12
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=zyBooks My library > MAT 350: Linear Algebra home > 2.12: MATLAB: LU Decomposition
Utilize the following linear system of equations for this activity.
x₁ + 2x₂ + 3x3 = 9
3x₁ x3 = 3
2x₁x₂ + x3 = 8
zy Section 2.12 - MAT 350: Linear Algebra
Note: Not all matrices have an LU decomposition. However, if the LU decomposition of a matrix doesn't exist, the rows of the matrix can
always be permuted to yield a matrix that does have an LU decomposition. Consider the system of equations Ax = b where A does not
have an LU decomposition. Let P be a permutation matrix (a matrix with a single 1 in each row and column). The permuted system of
equations PAX = Pb still has the same solution, just the order in which the equations are written down is now different. For the correct
permutation matrix, the matrix PA will have an LU decomposition. For more information, please see the MATLAB documentation for LU
matrix factorization.
Script
1%I need help with all of this, I feel I'm not doing this right.
14 y = L\b
15 x1 = U\b
4 %Create the coefficient matrix A and and the column matrix b of constants.
5 A = [1 2 3; 3 -1; 2 -1 1]
6 b = [9; 3; 8]
7
8 %Use the lu() command to find the LU decomposition of A, storing the lower and upper matrices
9 %in L and U, respectively.
10 [L, U] = lu(A)
11
발
Save
12 %Solve the system of linear equations Ax=b using the LU decomposition. Store the intermediary
13 %solution in y. Store the solution for x in x1.
C Reset
EPIC
GAMES
MATLAB Documentation
16 %Check that the solution x1 matches that found by directly using the backslash operator to solve
17 %the system Ax=b. Use the backslash operator to solve Ax=b in one step, storing the solution in x2.
18 x2 = U\y
19
O
▶ Run Script
K
?
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7/15/2022
Michael Pagano](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11714a3c-05a8-4e6b-af8b-597ead1dbb55%2F7003a9a3-6e51-4175-8d75-2a76df7907e2%2Frtpatrk_processed.png&w=3840&q=75)
Transcribed Image Text:←
b
D2L
zy
+
https://learn.zybooks.com/zybook/MAT-350-J6466-OL-TRAD-UG.22EW6/chapter/2/section/12
D21 Login Southern N...
The Chop Shop | Bu...
Type here to search
SNHU Bookstore
=zyBooks My library > MAT 350: Linear Algebra home > 2.12: MATLAB: LU Decomposition
Utilize the following linear system of equations for this activity.
x₁ + 2x₂ + 3x3 = 9
3x₁ x3 = 3
2x₁x₂ + x3 = 8
zy Section 2.12 - MAT 350: Linear Algebra
Note: Not all matrices have an LU decomposition. However, if the LU decomposition of a matrix doesn't exist, the rows of the matrix can
always be permuted to yield a matrix that does have an LU decomposition. Consider the system of equations Ax = b where A does not
have an LU decomposition. Let P be a permutation matrix (a matrix with a single 1 in each row and column). The permuted system of
equations PAX = Pb still has the same solution, just the order in which the equations are written down is now different. For the correct
permutation matrix, the matrix PA will have an LU decomposition. For more information, please see the MATLAB documentation for LU
matrix factorization.
Script
1%I need help with all of this, I feel I'm not doing this right.
14 y = L\b
15 x1 = U\b
4 %Create the coefficient matrix A and and the column matrix b of constants.
5 A = [1 2 3; 3 -1; 2 -1 1]
6 b = [9; 3; 8]
7
8 %Use the lu() command to find the LU decomposition of A, storing the lower and upper matrices
9 %in L and U, respectively.
10 [L, U] = lu(A)
11
발
Save
12 %Solve the system of linear equations Ax=b using the LU decomposition. Store the intermediary
13 %solution in y. Store the solution for x in x1.
C Reset
EPIC
GAMES
MATLAB Documentation
16 %Check that the solution x1 matches that found by directly using the backslash operator to solve
17 %the system Ax=b. Use the backslash operator to solve Ax=b in one step, storing the solution in x2.
18 x2 = U\y
19
O
▶ Run Script
K
?
EzyBooks catalog
88°F
? Help/FAQ
T
Bo
X
:
Other favorites
7:26 PM
7/15/2022
Michael Pagano
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