26. The following vectors (1, 1,0, 1), B= (1,0, 1, 2) , y= (3,0, 9, 3) are given in the inner product space V = Rª endowed with the standart inner product. (a) Find an orthogonal basis for the subspace W =< a, ß3,7 >. ( If you cannot find it, continue the question by assuming that {(1, 1,0, 1), (0,-1, 1, 1), (1, 2, 5, -3)} is an orthogonal basis for W.) (b) Find the orthogonal projection of (5,3, -1, 2).onto W (c) Find a basis for the orthogonal complement W of W.

26. The following vectors (1, 1,0, 1), B= (1,0, 1, 2) , y= (3,0, 9, 3) are given in the inner product space V = Rª endowed with the standart inner product. (a) Find an orthogonal basis for the subspace W =< a, ß3,7 >. ( If you cannot find it, continue the question by assuming that {(1, 1,0, 1), (0,-1, 1, 1), (1, 2, 5, -3)} is an orthogonal basis for W.) (b) Find the orthogonal projection of (5,3, -1, 2).onto W (c) Find a basis for the orthogonal complement W of W.

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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I, A and A?
26. The following vectors
a = (1, 1,0, 1), B= (1,0, 1, 2), y= (3,0, 9, 3)
are given in the inner product space V = R4 endowed with the standart
inner product.
(a) Find an orthogonal basis for the subspace W =< a, B,7 >. ( If you
cannot find it, continue the question by assuming that {(1,1,0, 1),
(0,-1, 1, 1), (1, 2, 5, -3)} is an orthogonal basis for W.)
(b) Find the orthogonal projection of (5, 3, -1, 2).onto W
(c) Find a basis for the orthogonal complement W of W.
27. Given the inner product
2.r191 + 3.r2y2 +3y3

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