Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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Subject : numerical methods Please write the code in c++. Provide code in text format so that I can run. Explain in detail.
6. Gaussian elimination algorithm can in principle be modified to
find solution to linear systems with singular matrices. In the
elimination stage, if all elements in the corresponding column are
zero, then that step can be ignored and we can go to the next
step. However, in such cases one of the diagonal elements in the
upper triangular factor U will be zero. During back-substitution
if it so happens that the corresponding numerator is also zero,
then the equations are consistent and the general solution can
be obtained by giving some arbitrary value to the corresponding
variable. In actual practice, it will be difficult to distinguish be-
tween zero and nonzero, but small elements. Try this algorithm
on the following system of equations:
2x1 + 5x2 + 8x3 + 9x4 = 10,
2x1 + 3x2 + 5x3 + 7x4 = 6,
xi + 5x2 + 8x3 + 7x4
10,
x1 + 2x2 + 3x3 + 4x4
4.
Find the null-space and the range of this matrix.
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Transcribed Image Text:6. Gaussian elimination algorithm can in principle be modified to find solution to linear systems with singular matrices. In the elimination stage, if all elements in the corresponding column are zero, then that step can be ignored and we can go to the next step. However, in such cases one of the diagonal elements in the upper triangular factor U will be zero. During back-substitution if it so happens that the corresponding numerator is also zero, then the equations are consistent and the general solution can be obtained by giving some arbitrary value to the corresponding variable. In actual practice, it will be difficult to distinguish be- tween zero and nonzero, but small elements. Try this algorithm on the following system of equations: 2x1 + 5x2 + 8x3 + 9x4 = 10, 2x1 + 3x2 + 5x3 + 7x4 = 6, xi + 5x2 + 8x3 + 7x4 10, x1 + 2x2 + 3x3 + 4x4 4. Find the null-space and the range of this matrix.
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