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. (1,-4,3)OB. (-4,3,1)OC. (3,- 7,5)O D. (2,-1,1)

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Answered: The coordinate vector of the vector…

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 (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1) B. (2,-1,1) C. (3,- 7,5) D. (1, -4,3) the vector basis
Find the coordinate vector (v)s relative to the basis S= {v ,,v,,v;} 21 for v = (2, 1, -2), if V, = (2, 2, -1) V2 = (-1, -2, 1) V3 = (1, -1, 1)
Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v = (13,54); B = {(1,0), (0, 1)} for R². (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.
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) OC. (3,-7,5) OD. (1,-4,3)
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: OA (2,-1,1) OB. (3,-7,5) OC. (1,-4,3) OD. (-4,3,1)
Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R = (0, 1, -1) 8 0-0-0- y = + S 8 Z -4 -6 + t
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)
(b) Example: Are the vectors;v₁ = (1, −1,0)), v₂ = (1, 3,−1) and v3 = (5,3,-2) linearly dependent?
Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (42, 34, 24); v1 = (4, 0, 0), v2 = (5, 5, 0), v3 = (8, 8, 8). (v)s =( i ). i i
Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (41, 39, 21); v1 = (7, 7, 7). (2, 0, 0), v2 = (6, 6, 0), v3 = (v)s=( i i i ).
Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1 + 2t, z = -2 O P(3,-1, -2), v = (-5,2,0) O P(-5,2,0), v = (3, 1, 2) O P(-3, 1, 2), v = (5,-2, 0) OP(5,-2, 0), v = (-3, 1, - 2)

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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: OA (1,-4,3) OB(-4,3,1) OC. (3,-7,5) OD. (2,-1,1)