Consider the following linear system: 1 2 X1 (6) 3 4 X2 Assume that, due to numerical error, the linear system (6) is solved with the same matrix, but with a slightly different right hand side: ]-[ 1 2 X1 3.01 (7) 4 X2 7.02 Without calculating the solutions of the linear systems (6) and (7), esti- mate the relative error in the 1-norm, || · ||1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the following linear system:
1 2
X1
3
(6)
X2
Assume that, due to numerical error, the linear system (6) is solved with the
same matrix, but with a slightly different right hand side:
1 2
X1
3.01
(7)
3 4
X2
7.02
Without calculating the solutions of the linear systems (6) and (7),
mate the relative error in the 1-norm, | : 1.
esti-
Transcribed Image Text:Consider the following linear system: 1 2 X1 3 (6) X2 Assume that, due to numerical error, the linear system (6) is solved with the same matrix, but with a slightly different right hand side: 1 2 X1 3.01 (7) 3 4 X2 7.02 Without calculating the solutions of the linear systems (6) and (7), mate the relative error in the 1-norm, | : 1. esti-
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