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 =81 +(4) z- (14, -3, 7, 4)(d)z =z =

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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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Find all Singular points of the given differential equation then classify as Irregular Singular Points ISP, or Regular Singular Points, RSP. (1– x²)y" – xy' + 3y = 0
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 = {(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
Given the base B= {(- 6,0,3), (- 21, –39, -42), (- 13,7,0)} in R, then the | R coordinates of the vector v= (- 96,120,114) in base B it is: O (10,6,6) O (10,-2,7) O (10,-2,6) (11,3,6)
For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and (3,13,-3)?
find the components of the vector P1P2. (a) P1(3,5) P2(2,8)
Sp
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
Find the cross product of the given vectors. 7) ах Ь a = (6,-6,-5) b=(-9,-1, 7) 8) а xЬ a = (9, 1, 2) b = (5, 3, 4) 9) u x v u= (5, 7, -2) v=(-7,-9,-5) 10) и x V u = (-6, -5, 4) v = (9,-8, 0)
Show that the vectors are orthogonal.

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each vector as a linear combination of the vectors in S. (If not possible, en s = {(6, -7, 8, 6), (4, 6, -4, 1)} (a) u = (6, 25, -20, -3) u 52 (ь) -10, 2 2