4. Suppose that xa is an approximate solution to the system of Ax = b. Let A, and I are nonsingular matrices, T-I- CA, and r is the residual vector for xa. Then for any natural norm, we have O O O (a) || e || < (b) ||e|| 2 (c) || e || ≤- || Cr|| 1-|| T|| (d) None of the above. a b O c C || Cr|| 1-|| T|| d ||CT|| 1-||T||

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 29CM
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4. Suppose that xa is an approximate solution to the system of Ax = b. Let A, and I are
nonsingular matrices, T-I- CA, and r is the residual vector for xa. Then for any natural
norm, we have
(a) || e || <-
|| Cr||
(b) || e ||1||||
|| Cr||
1-|| T||
(d) None of the above.
(c) || e || ≤-
a
|| Cr||
1-|| T||
O b
d
Transcribed Image Text:* 4. Suppose that xa is an approximate solution to the system of Ax = b. Let A, and I are nonsingular matrices, T-I- CA, and r is the residual vector for xa. Then for any natural norm, we have (a) || e || <- || Cr|| (b) || e ||1|||| || Cr|| 1-|| T|| (d) None of the above. (c) || e || ≤- a || Cr|| 1-|| T|| O b d
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