Show that the vectors u₁ = (3, 1,-4),= (3,1, –4), u₂ = (2,5,6), andu} == (1, 4, 8) form a basis in R³. Find the coordinates of (1, 1, 1)in this basis.

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Answered: Show that the vectors u₁ = (3, 1,-4), =…

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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Find the vector w of length 4 in the direction of v = 7i + 4j. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.)
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
Determine whether or not the given vectors in Rn form a basisfor Rna. v1 = (2, 0, 0, 0), v2 = (0, 7, 0, 0), v3 = (0, 0, 4, 6), v4 = (0, 0, 4, 2)b. v1 = (1, 7, −4), v2 = (3, 2, 5), v3 = (6, 5, 1), v4 = (0, 7, 4)
Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the standard basis vectors in R3. (c) Find -3u.
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)
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)
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)
Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.
Let the basis B = {b1, b2} and basis C = {c1, c2} where vectors b1 = (7 -2). b2 = 2 -1 , c1 = 4 1 c2= 5 2 Find the change of coordinates matrix from B to C. (b) Find the change of coordinates matrix from C to B.
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)

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Show that the vectors u₁ = (3, 1,-4), = (3,1, –4), u₂ = (2, 5, 6), and u} = = (1, 4, 8) form a basis in R³. Find the coordinates of (1, 1, 1) in this basis.