Let B= (b,.b2} and C = (c1,c2} be bases for a vector space V, and suppose b, = 3c, - 7c2 and b2 = 5c, - 6c2.a. Find the change-of-coordinates matrix from B to C.b. Find [x]c for x= 4b, - 5b2. Use part (a).а. РC-Bb. [x]c(Simplify your answer.)

Let us consider a vector space V and B and C be the basis of vector space then the vector of B can…

Answered: Let B = (b, ,b2} and C = {c,,c2} be…

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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1. Find three vectors that span the vector space given. 2. Consider the matrix A (attached photo) a. Determine if the columns of A are linearly dependent or independent. b. Find a set of vectors that span the solution space of AX = 04x1
Let 03 = If possible, express w as a linear combination of the vectors 1, 02 and 3. Otherwise, enter DNE. For example, the answer w = 401+502+603 would be entered 4v1 + 5v2 + 6v3. w =
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Find the image of the vector = (1, 2) by rotating it 30° counter-clockwise and scaling it by a factor of 4. Select all answers that are correct. O 2sqrt(3)-4 is the first component O 2+4sqrt(3) is the second component O 2sqrt(3)-4 is the second component O 2+4sqrt(3) is the first component none of these above
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Let A= {a;.a2,a3} and B = {b,.b2.b3} be bases for a vector space V, and suppose a, = 5b, - – 2b3. a. Find the change-of-coordinates matrix from A to B. b. Find (xlg for x= 5a, + 6a2 + az. a P B-A b. xlg =0 (Simplify your answer.)
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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Let B = (b, ,b2} and C = {c,,c2} be bases for a vector space V, and suppose b, = 3c, - 7c2 and b, = 5c, - 6c2. a. Find the change-of-coordinates matrix from B to C. b. Find (x)c for x = 4b, – 5b2. Use part (a). P = C-B a. b. [x]c (Simplify your answer.)