(i) Let ž. be an approximate solution. Calculate the relative forward error, relative back- ward error, and error magnification factor for this approximate solution (use infinity norm). (ii) Find the condition number of matrix A (using infinity norm). (ii) For a system of linear equations Af = b, what is the possible consequence of an extremely large condition number of A?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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5.(10 pts) Given that =
is the exact solution of the linear system of equations Ai = 6
with
-2
1
A =
2
-3
(i) Let ze
be an approximate solution. Calculate the relative forward error, relative back-
ward error, and error magnification factor for this approximate solution (use infinity norm).
(ii) Find the condition number of matrix A (using infinity norm).
(iii) For a system of linear equations A = 6, what is the possible consequence of an extremely large
condition number of A?
Transcribed Image Text:5.(10 pts) Given that = is the exact solution of the linear system of equations Ai = 6 with -2 1 A = 2 -3 (i) Let ze be an approximate solution. Calculate the relative forward error, relative back- ward error, and error magnification factor for this approximate solution (use infinity norm). (ii) Find the condition number of matrix A (using infinity norm). (iii) For a system of linear equations A = 6, what is the possible consequence of an extremely large condition number of A?
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