5. Consider the three linearly independent vectors uj = and let W C Rª be the span of B = {u1, u2, u3}. (1,0, 0, 0), u2 = (0, 1,0, 1), and u3 = (0,0, 2, 2), (a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' = {v1, V2, V3} which is orthonormal with respect to the dot product. (b) Express (2, 3, 2, 5) e W as a linear combination of the vectors in B'.

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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5. Consider the three linearly independent vectors uj =
and let W C Rª be the span of B =
(1,0,0,0), u2 = (0, 1,0, 1), and u3 =
(0,0, 2, 2),
{u1, u2, u3}.
(a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' =
orthonormal with respect to the dot product.
{V1, V2, V3} which is
(b) Express (2, 3, 2, 5) e W as a linear combination of the vectors in B'.
Transcribed Image Text:5. Consider the three linearly independent vectors uj = and let W C Rª be the span of B = (1,0,0,0), u2 = (0, 1,0, 1), and u3 = (0,0, 2, 2), {u1, u2, u3}. (a) Apply the Gram-Schmidt algorithm to the basis B to produce a new basis B' = orthonormal with respect to the dot product. {V1, V2, V3} which is (b) Express (2, 3, 2, 5) e W as a linear combination of the vectors in B'.
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