) Let S = span {u, v}. For each of the following sets of vectors determine whether S is a line or a plane.Select an Answer 1.-2-3-0-8,V=-2-4==Select an Answer 2.-51-8-85Select an Answer-5-4-8-8,V=-3Select an Answer 4.u=u=4-1-3-4, U =-6-103113.-11312

The given set is S=spanu, v We have to determine S is a line or a plane.

Answered: *) Let S = span {u, v}. For each of the…

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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28. How are lines expressed as vectors? a. Express 2 points along the line as vectors from the origin, then dot product the vectors b. Express 2 points along the line as vectors from the origin, then cross product the vectors c. Express 2 points along the line as vectors from the origin, then subtract the vectors d. Express 2 points along the line as vectors from the origin, then add the vectors
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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 S = span {u, v}. For each of the following sets of vectors determine whether S is a line or a plane. Select an Answer 1. u= u= -2 -3 -2 u= ,V= -4 -6 Select an Answer 2. -5 1 -0-8 5 -4 -10 3 11 Select an Answer 3. -5 -4 -0-8 -3 Select an Answer 4. 4 -1 -8-8- ,V= -3 -11 3 12