6. Let V = R² and let S be the set of vectors{[: I:}11|S = {v1,V2,V3} =-3-1|Is S is linearly independent? Explain why or why not.Does S span R2? Explain why or why not.Is Sa basis for R2? Explain why or why not.a.b.С.

We have V=ℝ2, S={v1, v2, v3}={12, -32-3, 1-1} We will first check if the set is linearly…

Answered: 6. Let V = R? and let S be the set of…

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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Is Sa Let V = R2 and let S be the set of vectors С. 5. %3D 1 S = {v1,V2} : %3D 2 -3 Is S is linearly independent? Explain why or why not. Does S span R2? Explain why or why not. Is Sa basis for R2? Explain why or why not. Let V = R² and let S be the set of vectors a. b. С. 6. %3D
For what values of a is the vector (a2, a, 1) belongs to span {x1 = (1,2, 3), x2 = (1,1,1), x3 = (0, 1,2)}? 3.
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Let u be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. A. span{u₁, U₂, U3 } = span{U₁, U₂, U3, U4 } . B. We only know that span{u₁, U₂, U3} C span{U₁, U₂, U3, U4 } . C. There is no obvious relationship between span{u₁, U₂, U3} and span{u₁, U2, U3, U4}. D. span {u₁, U₂, U3} = span{u₁, U₂, U3, U4} when none of {u₁, U₂, U3, } is a linear combination of the others. E. span{u₁, U₂, U3} is a proper subset of span{u₁, U₂, U3, U4 } . F. We only know that span{u₁, U2, U3, U4} C span{u₁, U₂, U3} . G. none of the above
Suppose wi and w2 are linearly independent. Let W span(w1, w2) and u = projw v where v is a vector not in W. Which of the following vectors is equal to the projection of v onto w, i.e., proj v? й - proja, v v – proj, v projw v None of the above.
Let u, v, w be three linearly independent vectors in R7. Determine a value of k, so that the set S = {u – v, v − 2w, w – ku} is linearly dependent. - k= =
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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6. Let V = R? and let S be the set of vectors {[:] S = {v1,V2, V3} -3 Is S is linearly independent? Explain why or why not. Does S span R?? Explain why or why not. Is Sa basis for R2? Explain why or why not. a. b.