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Find the LDU factorization of -3 -6 A -15 -29 33 -15 22 That is, write A = LDU where L is a lower triangular matrix with ones on the diagonal, D is a diagonal matrix, and U is an upper triangular matrix with ones on the diagonal. L = D = U =

Find the LDU factorization of -3 -6 A -15 -29 33 -15 22 That is, write A = LDU where L is a lower triangular matrix with ones on the diagonal, D is a diagonal matrix, and U is an upper triangular matrix with ones on the diagonal. L = D = U =

Advanced Engineering Mathematics
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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**Find the LDU Factorization** We are given the matrix: \[ A = \begin{bmatrix} -3 & -6 & 6 \\ -15 & -29 & 33 \\ -9 & -15 & 22 \end{bmatrix} \] Our goal is to factorize it as \(A = LDU\) where: - \(L\) is a lower triangular matrix with ones on the diagonal. - \(D\) is a diagonal matrix. - \(U\) is an upper triangular matrix with ones on the diagonal. ### Matrices to find: \[ L = \begin{bmatrix} 1 & & \\ & 1 & \\ & & 1 \end{bmatrix} \] \[ D = \begin{bmatrix} & & \\ & & \\ & & \end{bmatrix} \] \[ U = \begin{bmatrix} 1 & & \\ & 1 & \\ & & 1 \end{bmatrix} \]
Transcribed Image Text:**Find the LDU Factorization** We are given the matrix: \[ A = \begin{bmatrix} -3 & -6 & 6 \\ -15 & -29 & 33 \\ -9 & -15 & 22 \end{bmatrix} \] Our goal is to factorize it as \(A = LDU\) where: - \(L\) is a lower triangular matrix with ones on the diagonal. - \(D\) is a diagonal matrix. - \(U\) is an upper triangular matrix with ones on the diagonal. ### Matrices to find: \[ L = \begin{bmatrix} 1 & & \\ & 1 & \\ & & 1 \end{bmatrix} \] \[ D = \begin{bmatrix} & & \\ & & \\ & & \end{bmatrix} \] \[ U = \begin{bmatrix} 1 & & \\ & 1 & \\ & & 1 \end{bmatrix} \]
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