In P2, find the change-of-coordinates matrix from the basis B = (1- 2t +t,3 - 5t + 4t,2- 2t + 5t} to the standard basis C = {1,t,t}. Then find the B-coordinate vectorfor 1-2t +21?.In P2, find the change-of-coordinates matrix from the basis B = {1- 2t + t,3 - 5t + 4t,2 - 2t + 5t} to the standard basis C =1- 2- 52C-B145(Simplify your answer.)Find the B-coordinate vector for 1- 2t + 2t.[x]B(Simplify your answer.)

Answered: Image /qna-images/answer/1214b626-5f5e-4625-aa3a-f895f3297960.jpg

Answered: , find the change-of-coordinates matrix…

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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Answer only part c
Oa + Ob + 0c +4d la + (-1) b+ (-2) c +4d 0a+1b+ (-2) c +5d la + (-1) b + (-2) c + 2d 2a + 1b+ (-10) c +4d Then an orthogonal basis for Range(T) would be: Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 1) Let T a [25] =
The third column of the change of basis matrix from the basis B={r= (1,1,1); v= (1,0,1); w= (0,1,1) } to the basis p'={r=(3,4,1); x= (3,0,1);t=(-4, - 1,- 2) is: caqe OA 1 1 0C (2 1 OD (-3
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
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.
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.
Find the coordinates of x = {-10, 2, 4} with respect to the basis consisting of u, {1, 3, 2}, u, = {2, 1, 4}, and u; = {1,0, 6}. -
Consider the following matrix and vector: 1 1 1 -4 0 -3 A = -2 and x= x3 Given that Ax=0 and x3=-1, find x2. O-1 O1 2 O-2
How do I solve this in steps?
Find the matrix of the quadratic form S+7-3r-6r ay+4rd-2r2y a) 2-1 b) 7-2 7/2 -3/2 3. c) 7/2 -3/2 2. d) 410
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.
The third column of the change of basis matrix from the basis B= {u=(1,1,1) ; v= (1,0,1); w=(0,1,1 } to the basis B'= {r= (3,4,1); s= (3,0,1); t=(-4, -1, -2) is:

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