Let S = {u1, uz2, U3, U4} C Rª, where (1,1, 1, 1), U2 = (1, 1, – 1, –1), (1,—1,1, —1), и4 — (1, –1, –1, 1). U1 U3 (a) Show that S is orthogonal and is a basis for Rt. (b) Write v = (1, 3, –5, 6) as a linear combination of u1, U2, U3, U4. (c) Find the coordinates of an arbitrary vector v = (d) Normalize S to obtain an orthonormal basis for R4. (a, b, c, d) in Rª relative to the basis S.

Let S = {u1, uz2, U3, U4} C Rª, where (1,1, 1, 1), U2 = (1, 1, – 1, –1), (1,—1,1, —1), и4 — (1, –1, –1, 1). U1 U3 (a) Show that S is orthogonal and is a basis for Rt. (b) Write v = (1, 3, –5, 6) as a linear combination of u1, U2, U3, U4. (c) Find the coordinates of an arbitrary vector v = (d) Normalize S to obtain an orthonormal basis for R4. (a, b, c, d) in Rª relative to the basis S.

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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Let S = {u1, U2, U3,
U4} C Rª, where
u1 = (1, 1, 1, 1),
и2 —D (1,1, —1, -1),
из 3D (1, —1,1, —1), и4 —
= (1,–1, –1,1).
(a) Show that S is orthogonal and is a basis for R'.
(b) Write v =
(1,3, –5, 6) as a linear combination of u1, U2, U3, U4.
(c) Find the coordinates of an arbitrary vector v =
(a, b, c, d) in R4 relative to the basis S.
(d) Normalize S to obtain an orthonormal basis for R4.

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