In the Euclidean inner product space R4 with an orthonormal basisB={(1,1,1,1),(1,1,-1,-1). (1,-1,-1,1).(-1.1-1.1}the fourth component of the coordinate vector of the vector u= (1,2,4,6) is ...A. None in the given list.B. 6C. 39. 11/1/20D.OF 2/1/2E.

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Answered: In the Euclidean inner product space 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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The coordinate vector of the vector (-4,3,1) in the basis B = {u= (1,1,1); v= (1,0,1); w= (0,0,1) } is : O A. (2,-1,1) OB. (-4,3,1) O C. (1,-4,3) D. (3,- 7,5)
Do the vectors form a basis for R"? Show which conditions, if any, are met, and show which conditions, if any, are not met. Be sure to address all conditions of a basis. a) v1 = (1,3, –2), v2 = (-2,–6,4) b) v1 = (2,1,0,3), v2 = (0,1,5,7), v3 = (0,0,3, –1), v4 = (0,0,0, –4)
The coordinates for the vector v = (1,2,4) relative to the standard basis B = {(1,0,0), (0, 1,0), (0,0,1)} is [v] B = (1,2,4). The coordinates for v relative to the nonstandard basis B' = {(1, 0, -1), (2,1,-1), (-2, 1,4)} is [v]B¹ = (9,−1,3). Find the transition matrix P-1 from B to B' and show that this does change the coordinate of v relative to B to the coordinate of v relative to B'.
5. Determine the courdinate vector of V =(8,-4,-12) velative to the basis S = {C,,1),(1,s,-3), (2,2,113
1. Vectors v1 = (1,1,1,1,0), v2 = (-1,1,0,0,0), v3 = (1,1,-1,-1,0), v4 = (0,0,2,-2,0) and v5 = (0,0,0,0,2) form an orthogonal basis for a of R5 and X = (-3, -2,5,1,-4). Find the coordinates of X with respect to the given basis.
a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x) = -3x² + 2x – 5 , and q(x) = -x+5x? b) Verify that the basis set S = {(3,0,4), (-4,0,3), (0,1,0)} is orthogonal then find the coordinates of the vector u = (-5,5,1) using inner product
(3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or linearly dependent? Given vectors v, = (2, –4,5). b) Do the vectors form a basis for R3? Why or why not?
Find the coordinates of vector u=(4,5) with respect to linear basis ((2,1),(1,-1)] ? a. 2 b. 3 O c. -2 d. -3 -1
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D
The coordinate vector of the vector (1,2,2) in the basis B = {u= (1,1,1); v = (1,0,1); w= (0,0,1) } is : O A. (1,2,2) O B. (2,-1,1) O C. (2,1,3) O D. (1,2,1)

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In the Euclidean inner product space R4 with an orthonormal basis B={-(1,1,1,1), ½-(1,1, − 1,− 1), — (1,-1,-1,1), (-1,1,-1,1)} - the fourth component of the coordinate vector of the vector u = (1,2,4,6) is ...