Let S 3D {u1, и2, из, ид} С RA, where (1, 1, 1, 1), из %3D (1,1, —1, —1), из %3D (1,—1,1, —1), и4 (1,–1, –1, 1). U1 (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 3D {u1, и2, из, ид} С RA, where (1, 1, 1, 1), из %3D (1,1, —1, —1), из %3D (1,—1,1, —1), и4 (1,–1, –1, 1). U1 (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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