Let S = {u1, u2, U3, U4} C Rª, where (1,1, 1, 1), и2 %3 (1,1, —1, —1), из —D = (1,–1,1, –1), (1, –1, –1, 1). U4 = (a) Show that S is orthogonal and is a basis for R4. (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 Rª relative to the basis S. (d) Normalize S to obtain an orthonormal basis for R4
Let S = {u1, u2, U3, U4} C Rª, where (1,1, 1, 1), и2 %3 (1,1, —1, —1), из —D = (1,–1,1, –1), (1, –1, –1, 1). U4 = (a) Show that S is orthogonal and is a basis for R4. (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 Rª relative to the basis S. (d) Normalize S to obtain an orthonormal basis for R4
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 just solve the last one - part d. Thank you
Transcribed Image Text:Let S 3D {u1, и2, из, ид} С R, where
U1 =
: (1,1, 1, 1), и2 %3D (1,1, —1, —1), из 3D (1,—1,1, -1),
и4 3 (1, —1, —1, 1).
(a) Show that S is orthogonal and is a basis for R4.
(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 Rª relative to the basis S.
(d) Normalize S to obtain an orthonormal basis for R4.
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