Which of the following are true statements?If {y, z} is linearly dependent, then {x, y, z} is 'linearly dependent for any X.Every set containing a spanning set is again a spanning set.If {x, y, z} is linearly independent, then {y, z} is linearly independent.If all of X1, X2,..., Xk are nonzero, then {X1, X2,...,xk} is linearly independent.If {x, y} is linearly independent, then {x, y, x+y} is linearly independent.If one of X1, X2,..., x is 0, then {x, y, z} is linearly dependent. If {x, y, z} is linearlyindependent, then ax+by+cz = 0 for some a, b and c in R.

We can analyze each statement one by one: Step 1: (Statement 1) True. If {y, z} is linearly…

Answered: Which of the following are true…

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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3. Given set A={1,2,3,4,5) and let R and S be a binary relation on set A. {(a, b) e AxA | bla} and S = {(2,1), (2,3), (3,4), (3,5), (4,5)} a.) Evaluate the Domain and Range of SoR. b.) Evaluate (SOR)-¹ and SoR.
3. Suppose that A, B C R². (a) If A and B are homeomorphic, are A and B homeomorphic? (b) If A and B are connected and homeomorphic, are Aº and Bº homeomorphic?
1. Let S = {(1, 1), (1, 2), (2, 1), (3, 2), (3, 3)}. Consider the polytope conv(S). Write this set as {x | Ax 0}, where A has 3 rows.
Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show that the translated set {Pi + q, P2 + q, P3 + q} is also affinely independent.
Let (u, v) be a minimum-weight edge in a connected graph G. Show that (u, v) belongs to some minimum spanning tree of G.
Which of the following are spanning sets for R³? Justify your answer. (a) {(1, 0, 0), (0, 1, 0), (0, 0, 1)} (b) {(1, 0, 0), (0, 2, 2), (1, 1, 1)} (c) {(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1)} (d) {(1, 0, 0), (0, 1, 1), (1, 0, 1)} (e) {(1, 1, 1), (0, 0, 1)}
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Consider X = {a1, a2, ..., an}Can a topology of X with 3 open and one with 4 open be equivalent?
a) Consider the set S= {+1, +t, t+1). Detrmine whether p(t)= 3t-5t+3 belongs to span S. b) Determine whether {r +1, -t, t+1} is a spanning set.
topology
2. Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a, b) = (a₁, b₁) if a = a₁. (d) (a, b) = (a₁, b₁) if a - b = a₁-b₁.

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