a) Determine whether S = {(1,0, – 1), (2,1,0), (3,1, – 1), (1,1,1)} spans.R³.= {(c²,0,1), (0, c, 0), (1,2,1)} is a linearlyb) Find all c ER for which sindependent set of vectors in R³.c) Determine whether W = {(x, y, z) E R°| x² + y? = z²} is a subspaceof R³.

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Answered: a) Determine whether S = {(1,0, -1),…

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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Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear combirnation to span (x, y, z). If they do not, give a specific vector they do not span.
Find nonzero vectors a, b, and c in space such that a × b = a X c but b c.
The linear combinations of v = (a,b) and w = (c,d) fill the planes unless _______. Find four vectors u,v,w,z with four components of each so that their combinations cu+dv+ew+fz produce all vectors ( b1,b2,b3,b4) in four dimensional space.
The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent. What is a valid expression of the last vector as a linear combination of the others? a. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)-(0,0,1,1) b. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) c. (1,0,1,1)=-(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) d. (1,0,1,1)=2(1,1,0,0)+2(0,-1,0,0)+2(0,0,1,1)
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)
Consider the set of vectors S= {u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3). Is the vector b= (12,-2, -11) a linear combination of the vectors in the set S? If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary calculations. Does the set S span R³? I in R², where Given the linear transformation T: R² R³ defined by T(x) = Ax for all x A = [u₁ U₂] 1-2 0 3 -1 2 does T map R² onto R³? Circle your choice below and briefly justify your answer. Circle One: [Onto / Not onto
1.4 Please answer these (a,b,). Explain well your calculations and steps! Thank you!!! A)Expresses the vector u = [-2,5,-1] as a linear combination of v = (1,3,0] and w = [8, -9,3]. B)Checks whether the vectors p = [0,4,-3], q = [-2,-4,1] and r = [-1,6, -3) are coplanar. Either to = [-2,-3,2] and b = [0, -4,1]. C)Determines an orthogonal vector to a and b.

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a) Determine whether S = {(1,0, -1), (2,1,0), (3,1,-1), (1,1,1)} spans. R³. b) Find all c E R for which S = {(c²,0,1), (0, c, 0), (1,2,1)} is a linearly independent set of vectors in R³. c) Determine whether W = {(x, y, z) € R³| x² + y² = z²} is a subspace of R³.