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(d) Explain why each vector VER can be expressed in precisely one way as v u+w, where u ES and w ES.

(d) Explain why each vector VER can be expressed in precisely one way as v u+w, where u ES and w ES.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve part  d only

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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