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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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 10EQ: In Exercises 7-10, show that the given vectors form an orthogonal basis for2or3. Then use Theorem...
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Please just solve the last one - part d. Thank you

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.
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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