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Select the correct statements from below for a linear system of equations Ax = b. The determinant of a permutation matrix is negative if it leads to an odd number of row interchanges in Gaussian elimination. A zero in the pivot position upon pivoting implies that the matrix A is singular. If A is a lower triangular matrix then the system could be solved by back-substitution. The number of floating point operations in back-substitution is of order O(n³). If the LU decomposition for A is given then the systems could be solved in O(n²) operation.

Select the correct statements from below for a linear system of equations Ax = b. The determinant of a permutation matrix is negative if it leads to an odd number of row interchanges in Gaussian elimination. A zero in the pivot position upon pivoting implies that the matrix A is singular. If A is a lower triangular matrix then the system could be solved by back-substitution. The number of floating point operations in back-substitution is of order O(n³). If the LU decomposition for A is given then the systems could be solved in O(n²) operation.

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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Select the correct statements from below for a linear system of equations Ax = b. The determinant of a permutation matrix is negative if it leads to an odd number of row interchanges in Gaussian elimination. A zero in the pivot position upon pivoting implies that the matrix A is singular. If A is a lower triangular matrix then the system could be solved by back-substitution. The number of floating point operations in back-substitution is of order O(n³). If the LU decomposition for A is given then the systems could be solved in O(n²) operation.
Transcribed Image Text:Select the correct statements from below for a linear system of equations Ax = b. The determinant of a permutation matrix is negative if it leads to an odd number of row interchanges in Gaussian elimination. A zero in the pivot position upon pivoting implies that the matrix A is singular. If A is a lower triangular matrix then the system could be solved by back-substitution. The number of floating point operations in back-substitution is of order O(n³). If the LU decomposition for A is given then the systems could be solved in O(n²) operation.
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