Let u = : (3, 6, 2), v = (6, 7, −2), w = (24, 33, h + 0).Determine the value for h so that w is in the span of the vectors u and v.h =Determine the value for h so that u is in the span of the vectors v and w.h =1. If h equals the value in the first question above, determine whether orSelect an Answernot the set {u, v, w} is linearly independent.

Answered: Image /qna-images/answer/8342a9c1-d206-4487-8251-dae7b295cc12.jpg

Answered: Let u = (3, 6, 2), v = - (6, 7, -2), w…

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 figure below shows two named points A and B in R?. 6 4 A -1 -2 -3 -4 B -5 -6 -6 -5 -4 -3 -2 -1 5 6 1 3 4 > Part 1 Part 2 a. Write the vector BA as a sum of two vectors, one parallel to (1,0) and the other parallel to (0, -2). ВА- + b. Write the vector BA as a sum of two vectors, one parallel to (1, 1) and the other parallel to (-1, 1). BA = +
Please answer and write correctly and neatly. Let u = (-1, 3), v = (2, 4), and w = (2, -5). Find the component form of the vectora) u + vb) u - wc) 3u + 2wd) 2u - 4ve) -4u - 3v Please follow the format in the image below.
State if the following statement is true or false. The set of vectors B={u= (2,7,3); v = (1,0,7) ;w=(3,7,-4)} spans R³. O True False
Consider the vectors , v = , and w=. Simplify the expressions on the left column and match its value on the right column. u = zu + v 2v - w w + (u + v) W zu (v - w) - U :: :: :: :: :: :: :: ::
Consider the set of vectors S= {u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3). Is the vector b= (12,-2, -11) a linear combination of the vectors in the set S? If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary calculations. Does the set S span R³? I in R², where Given the linear transformation T: R² R³ defined by T(x) = Ax for all x A = [u₁ U₂] 1-2 0 3 -1 2 does T map R² onto R³? Circle your choice below and briefly justify your answer. Circle One: [Onto / Not onto
Let v = (1,0, -2), v2 = (-2, 1,7), v3 = (h,-3,–5) be three vectors in R. For what value(s) of h is v, spanned by v, and y,? Answer: h = -3 h+-2 Ch#2 ch = 2 The co FINISH REVIEW
Show the diagram with labels and all the work necessary please!
a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =

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