................................................./...............................................,,......../..............................................please show work as neat and complete as possible.thanks in advance................................................../...............................................,,......../.............................................. Include every possible detail in the solutions of all problems.Be sure to check your notation.Either prove that the given set S is a subspace of the vector space V or demonstrate that Sis not a subspace of V.In your proofs, do not combine steps.Any time you rely on a property of real numbers, indicate which property of real numbersI.you are using to go from one step to the next.Do not use linear combinations when proving S is a subspace.Instead, treat vector addition and scalar multiplication separately, the way we did it in class.To demonstrate that S is not subspace, show that one of the ten criteria for being asubspace fails to hold true.1)S = {a + bx + cx²: a + 2b – 3c = 1; a, b, c € R}2)S %3D {a + bx + сx?: а + 2b — Зс %3D 0%; а, b, с E R}3)= {[: "]:« € (-», 0]}I.Find a set of vectors S that spans the vector space V.Begin by parameterizing V; show your work.r2r – s1)V =3r + t: r, s,t E Zwith the usual operations from R°4r + 6s – t2)V =: 2a – d = 0, -2a + c – 2b + d = 0; a, b, c, d e Z }with the usual operations from M22

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Answered: 1) S = {a + bx + cx²: a + 2b – 3c = 1;…

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1) S = {a + bx + cx²: a + 2b – 3c = 1; a, b, cE R} 2) S = {a + bx + cx²: a + 2b – 3c = 0; a, b, c E R} 3)

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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.........................ASAP..................Thank You...........................I need answers ASAP............. A distribution of Garden supplies process plant food by mixing two ingredients A and B. The final product must weigh exactly 10lbs. Different amounts of estimated specifications are such that every unit of the items must contain a minimum of 4 and a maximum of 7lbs of ingredients od A, and a minimum of 3 and a maximum of 6 lbs of ingredients for B. Ingredients A and B each cost $0.35 per pound. What should be the composition of the Final product?Min Z=0.35x1+0.35x2Subject to:x1+x2=0x1>=4,x1<=7x2>=3,x2<=6x1,x2>=0
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