6. Let x#0 and y‡0. (a) If x ¹ y, show that {x, y} is a linearly independ-ent set. (b) Extend the result to mutually orthogonal nonzero vectorsX1,Xm2

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Answered: 6. Let x#0 and y‡0. (a) If x 1 y, show…

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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Q3) Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies the relation ž. (2ï – j + R) = -6. А) (2, -6, —3) B) (-1,2,0) C) (-3,3,3) D) (2, –2, – 1) E) (1,–1,–1)
3. Suppose u and v are two vectors in R and u v. Which of the following options are possible for Span{u, v}? Select yes or no for each option. (a) A point (b) A line (c) A plane (d) R3 Enter your answer for (a) here: [Select ] Enter your answer for (b) here: [ Select] Enter your answer for (c) here: [Select ] Enter your answer for (d) here: [ Select ]
(13.) Determine whether the vectors span the vector space. (a.) Let u = 2-5t+6t²-t³,v=3+2t-4t² (b.) Let vectors of P3(t). 1 2i -=(²²). -- (28) V= 5 i U= vectors of M2x2(C) over R. (c.) Let u = (2,0), v = (i, 1), w = (0, 2i), y = (1, 1) be the vectors of C² over R.
9. Is the set of vectors {(-2, 2, 0), (1, 1, 1), (8, -4, 2)} over R linearly dependent or independent? Why?
18. Find the orthogonal projection of the vector a = (-9, -8, 7) in the direction of the vector b = (-3,-5,-2).
Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”. Fill in the blanks so that the following statements are true. If you believe you don't have enough information to conclude anything for any of the cases, choose the answer "???". Note that there is no intended relationship between the parts. In each case, assume only what the statement says to assume. If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and S C U, then dim(U) 3. If S' is a spanning set for U, then dim(U) 3. If span(S) = U then S If S is a basis for U, then S linearly independent. linearly independent.

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6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the result to mutually orthogonal nonzero vectors X1, Xm. 9