Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)S = {(2, 1, 3), (5, 0,4)}(a) Z =Z =V =(b) v-(18,-)4W == (1, -3, 5)(d)(c) w = (4, -7, 13)U=V=) ₁₁ + ( [5950)u =(3, 1, -1)+)5₁ + (

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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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Are the vectors = [1 21], [3 2 -3] and @= [2 3 -5] linearly independent? linearly independent If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true. w = 0. ū+ v+
4. (a) Determine if the four points P1: (1,1,- 2), P2: (4,0,- 3) P3 :(1,-5,10), and P4 : (-7,2, 4) lie on the same plane. (b)Two vectors are parallel if and only if they are nonzero scalar multiple of each other's. Find a vector ( b )that is parallel to a = 3i + 7j and has magnitude 2.
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)} (a) z = (3, -4, 8) Z = 1 27 (b) v = |8, 4 4 v = + (c) w = (3, -9, 15) w = (d) u = (7, 1, -1) u = +
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, –1, 3), (5, 0, 4)} (a) z = (1, -3, 5) S2 Z = 75 (b) 23, 4' 4 V = S2 V = (c) w = (6, -8, 16) %3D S2 W = (d) u = (9, 1, –1) S2 u = +
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(6, -7, 8, 6), (4, 6, -4, 1)} (a) u = (6, 25, –-20, -3) $1 + u = (4, 5 -10, 2) 41 75 (b) (c) (-4, -14, 23, 37) w = 8 1 + (4) z- (14, -3, 7, 4) (d) z = z =
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, 1, 3), (5, 0,4)} (a) z = (11,-8, 20) Z = (b) V = (c) W = (d) u = v = (18,-1, 50) W = (4, -7, 13) S₁ + u =(3, 1, -1) S₁ + )$₁ S1 + S₁ + ) $₂ S2
find the components of the vector P1P2. (a) P1(3,5) P2(2,8)
Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices. (2,0,-7), (10, 1, -7) (8, 5, -3), (40, 25, -15) O (-5, 0,7), (-1, 8, 7), (3, 4, 3), (-7,2,0) (2,0, 5), (2, -6, 7), (6, 3,9)
Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)) z=(5, -5, 11) z = (b) V = (c) w (3,-9, 15) W = (d) U= v = (13,-1, 43) )s₁ u= (1, 1, -1) + ) s₁ - + )S₁ + $₂ )$₂
given the vector A=48p-6.9åo+3â, at point P(6,8,5). The vector A can be expressed in cartesian system as O a. -3.12åx+7.34ây+3âz O b. -3.12åx+7.34ay-3az O.7.92áx+-0.94ay+3az O d. -7.92áx+-0.94ây+3áz O e.-7.92ax+-0.94ay-3áz

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Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, 1, 3), (5, 0,4)} (a) Z = = (1, -3, 5) Z = (b) V = = (18,- 1, 50) 4 W = V= (c) w = (4, -7, 13) + 1)₁₁ + ( [