3) Let S = {(1, –2, 2, 1), (2, –2, 1, 2), (–1, 5, 1, –1} C Rª. The span of S (i.e., the set of all linear combinations of the three vectors of S) is a three dimensional subspace Rª.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a)  Use the Gram-Schmidt orthogonalization process to find a set of three mutually orthogonal vectors {v1, v2, v3} that has the same span as S. Do not attempt to make these vectors to be unit vectors.

(b)  Let w = (5, 1, 2, 3). Find the projection of the vector w to the span of S. Deduce the rejection of w by the span of S.

(3) Let S = {(1, -2, 2, 1), (2, –2, 1, 2), (–1, 5, 1, –1} C Rª. The span of S (i.e., the set of all linear
combinations of the three vectors of S) is a three dimensional subspace Rª.
Transcribed Image Text:(3) Let S = {(1, -2, 2, 1), (2, –2, 1, 2), (–1, 5, 1, –1} C Rª. The span of S (i.e., the set of all linear combinations of the three vectors of S) is a three dimensional subspace Rª.
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