4. Determine if the set U of functions whose definite integral over (0,1) equals 5 is a subspace ornot. Consider the set of nxn matrices over the real numbers. Show this is a vector space. Anddetermine whether or not the following subsets are linear subspaces:a.Set of invertible matricesb.C.Set of matrices of trace =0.'Subset of D = {(a, 1/a, b) | a, b in R} in R³

Answered: Image /qna-images/answer/532a75db-7802-4df7-bca4-eb8bac769cbd.jpg

Answered: Determine if the set U of functions…

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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Which of the following are subspaces (mark all that apply)? let A be an m x n matrix and v1, v2, v3 be vectors in R^n a) The set of vectors x in R^n such that Ax =0 b) The set of vectors x in R^n such that Ax = b c) The span of the columns of A d) All the possible combinations of v1, v2, v3 e) [x y z] = t [ 1 -1 1] f) [x y z] = [3 -1 1] + t [3 2 1] + s[1 0 -1]
I.1. Find the adjoint of the matrix,then use the adjoint to find the inverse if possible 2.Find the Equation of (-4,0) and (4,4)3. Find the volume of the tetrahedron (2,0,0), (0,2,0), and (2,2,2).II.4. Determine whether the set of W is a subspace of R^3 with the standard operation. Justify your answer. a. b.5. Determine whether the set S is linearly independent or linearly dependent.a.b.c.
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Show that Null Space of Ax = 0 is a subspace.
Is this a subspace of R3? Please explain it.
Fill in the blank with an integer. The distance of (5, −3, 5) to the subspace spaned by {(2, 0, −1), (2, −5, 4)} is
Consider three linear subspaces of R³: W₁ = R(1,0,1,0,1) W₂ = {(x-z,-x,y-z,-y,x+y-z): x,y,z ER} W3 = {(x1, x2, x3, x4, x5) ERS: -x1 + x2 = −X3, X5-X3 = X4₁X1 - xs=0} (a) Find basis vectors for W; for i=1,2,3. (b) Determine what are the dimensions of W; for i=1,2,3. (c) Define W=W₁ W₂ W3. What is the dimension of W. Find a basis of W.
et △ABC be a triangle in S^2 (the two-dimensional sphere). Let the dual point C'∈S^2 of C be defined by the following three conditions:(i) d(C' , A)=π/2(ii) d(C' , B)=π/2(iii) d(C' , C)≤π/2A' and B' are defined analogously. Thus we get a dual triangle △A' B' C'. More precisely, △ABC is a non-degenerate triangle, andit follows (you may assume) that △A' B' C' is too.(question) Are there triangles △ABC in S^2 identical to their own dual △A'B'C'? I would be very thankful if you could provide some explanation with the steps, thank you in advance.

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