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faced with the following coefficient matrix of a system of equations to be solved by iterative methods, 10 -1 -3 -2 33 -7 -6 -3 -27. do you have. any guarantee that you will obtain a solution? cannot tell because the matrix is not symmetric there are no guarantees in life O can't determine because the off-diagonal coefficients are all negative O yes, because the matrix is diagonally dominant O no, because the matrix is not diagonally dominant

faced with the following coefficient matrix of a system of equations to be solved by iterative methods, 10 -1 -3 -2 33 -7 -6 -3 -27. do you have. any guarantee that you will obtain a solution? cannot tell because the matrix is not symmetric there are no guarantees in life O can't determine because the off-diagonal coefficients are all negative O yes, because the matrix is diagonally dominant O no, because the matrix is not diagonally dominant

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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Question 1 faced with the following coefficient matrix of a system of equations to be solved by iterative methods, 10 -1 -3 -2 33 -7 -6 -3 -27 do you have any guarantee that you will obtain a solution? cannot tell because the matrix is not symmetric there are no guarantees in life O can't determine because the off-diagonal coefficients are all negative O yes, because the matrix is diagonally dominant O no, because the matrix is not diagonally dominant
Transcribed Image Text:Question 1 faced with the following coefficient matrix of a system of equations to be solved by iterative methods, 10 -1 -3 -2 33 -7 -6 -3 -27 do you have any guarantee that you will obtain a solution? cannot tell because the matrix is not symmetric there are no guarantees in life O can't determine because the off-diagonal coefficients are all negative O yes, because the matrix is diagonally dominant O no, because the matrix is not diagonally dominant
Expert Solution
Step 1

A square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix A is diagonally dominant if

where aij denotes the entry in the ith row and jth column.

If a strict inequality (>) is used, this is called strict diagonal dominance.

 

The Jacobi and Gauss–Seidel methods for solving a linear system converge if the matrix is strictly (or irreducibly) diagonally dominant.

 

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