Problem 1. Let c, C be the columns of the matrix b, ba and let b 3 ba (a) Find the matrix (A"A) 1. (b) Find necessary and sufficient conditions on the components of b in order the system Ax b be consistent. Find the least square solution for Ax (c) Let S Lin{C, C2). Find a basis of the orthogonal complement s' of S. (d) Explain why each vector v E IR can be expressed in precisely one way as v = u+ w, where u ES and wES. b. %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 1. Let C1, C2 be the columns of the matrix
1
and let b
3
b2
ba
2.
(a) Find the matrix (A"A) 1.
(b) Find necessary and sufficient conditions on the
components of b in order the system Ax = b be
consistent. Find the least square solution for Ax = b.
(c) Let S Lin{C1,C2}. Find a basis of the orthogonal complement
s' of S.
(d) Explain why each vector v EIR* can be expressed in precisely
one way as v =u+ w, where u ES and w ES.
Transcribed Image Text:Problem 1. Let C1, C2 be the columns of the matrix 1 and let b 3 b2 ba 2. (a) Find the matrix (A"A) 1. (b) Find necessary and sufficient conditions on the components of b in order the system Ax = b be consistent. Find the least square solution for Ax = b. (c) Let S Lin{C1,C2}. Find a basis of the orthogonal complement s' of S. (d) Explain why each vector v EIR* can be expressed in precisely one way as v =u+ w, where u ES and w ES.
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