13- 1- 3- 9- 8Let P =0 , v1 =Complete parts (a) and (b).-3 -5V2 =6.andV32%3D4147a. Find a basis fu,, u2, uz} for R° such that P is the change-of-coordinates matrix from fu,, U2, uz} to the basis (v,, v2, V3}. [Hint: What dothe columns ofP represent?]С+ В- 8- 4- 5u1- 6U2 =- 8, U3- 2%3D1821b. Find a basis {w,, w2, W3} for R° such that P is the change-of-coordinates matrix from (v1, v2, V3} to (w1, W2, W3}:W1W2, W3%3D%D

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Answered: 1 3 - 1 - 3 -9 - 8 Let P = - 3 -5 ,v1 =…

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
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)
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)
EXAMPLE 5 Vectors in R' Let u = (2, –4, 1) and v = ponents of the following vectors and draw them in R. (3, 0, – 1). Find the com- 1 b. -2v c. u + 2v а.
AB= <-1, 2, 0> BC= <0, -2, -3> Find a vector orthogonal to AB and BC.

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