1. Let {v₁,..., Vn} be a linearly dependent set. Prove that there exists some j with 1 ≤ j

Q: (e) Let A = {1,2, (3,4,5)), B=(2, 3, 4, 5, 6, 7). Find i. An B. A x B. P(AB), where P(X) is the…

A: According to the Bartleby guidelines I am answering only one first 3 parts.   We are given…

Q: Suppose v1, V2,..., Vm E V. Prove that {v1, v2, ..., Um} = (span(v1, v2, ..., Um))-.

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Q: Show that the set S= {(1, 2, 1), (3, 1, 5), (3, -4,7)} u de nendent where. SCV (B). is linearl

A: We need to find scalars c1, c2, and c3, not all zero, such that   c1(1, 2, 1) + c2(3, 1, 5) + c3(3,…

Q: Help with this please

A: The objective of this question is to prove that for any two bounded nonempty subsets of real…

Q: X, Y and Z be subsets of the set . Verify the following propert XU(YUZ) = (XUY)UZ, XN(YnZ) = (XnY)…

A: X, Y, Z be subset of a universal set Ω to verify…

Q: Suppose that the set {u, v} is linearly independent and that w is NOT in Span{u, v}. Using the…

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Q: Let XC Rn convex. Prove that x is an extreme point of X if and only if the set Cis convex, where X =…

A: Let X⊂ℝn be convex . To prove: x is an extreme point of X if and only if the set C is convex, where…

Q: 1. for  the Relation R ‘is a factor of’, on set A{1,2,3,6}. Write: A) the ordered pairs B) a…

A: Given the set A{1,2,3,6}

Q: (E, Q4: state and prove L is a normed space ? e a ne. Vila a convex set.

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Q: 5. Let V₁, V2, V3, and v4 be such that {V1, V2, V3} is linearly dependent and {v2, V3, V4} is…

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Q: b) A function g: Z → Zis defined by the rule g(m, n) = m + n Determine whether it is onto or not..

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: (a) {(1,0,0), (0, 1, 1), (1,0,1)¹} (b) {(2, 1,-2)T, (3, 2, -2), (2,2,0)¹}

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Q: Establish formally, whether the following set is open, closed, or neither closed nor open (justify…

A: We will use the basic knowledge of set theory and point-set topology to answer this question…

Q: Let S be the subset of the ℝ2 given by all pairs (x, y) so that x2 + y2 = 2. Show that S is a closed…

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Q: The reflexive closure of  R={(1,1),(2,1),(1,2)}R={(1,1),(2,1),(1,2)} on the set \( A=\lbrace{1,2,3…

A: The set A={1,2,3} The reflexive closure is obtained by adding a,a to R for each a∈R since (1,1) is…

Q: Let T={X, {a}, {a,b).{a,c,d}, {a,b,c,d}, {a,b,c}} be a topology on X=(a,b,c,d,e). (ii) Find N.…

A: Given : (X, T) be a topological space,  where  X = {a, b, c, d, e} and T = {X, ϕ, {a}, {a, b}, {a,…

Q: Let X and Y be two topological spaces. X is connected and Y is disconnected are they homotopy…

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Q: 2. Determine whether the set R2 with the operations (x1, y₁) + (x2, Y2) = (x1x2, 9192) and c(x₁, y)…

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Q: 9. S= {(6,2, 1), (-1,3,2)} is: %3D linearly independent set of R. b. a linearly dependent set of R3.…

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Q: The universal set is U with n(U)= 70, A and B are subsets of U with n(A)= 55, n(B)= 20 and n(A’…

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Q: 4. (a) Write down four distinct elements of the set {2 €C:2- E = 2i}.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: i). Find the highest normal form of a relation R(A,B,C,D,E) with FD set as (BC->D, AC->BE, B->E}

A: As we can see, (AC)+ = {A, C, B, E, D} but none of its subset can determine all attribute of…

Q: Q. Let S = {(x, y), x² + 4y2 = 4} CR2, then S - {point} is homeomorphic to – y? = 4} a. {(x, y), 4x2…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: Is T ={∅, X, {1, a}, {1, b}, {2, c}, {1, a, b}, {1}} a topology on X = {1, 2, a, b, c}? Why?

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Q: Let S be the subset of the ℝ2 given by all pairs (x, y) so that x2 + y2 = 2. Show that S is a closed…

A: Inverse image of closed set is closed. Whenever f is continous from that we solved this question.

Q: Suppose we have a set of vectors v_1...v_n such that v_1 could be written as a linear combination of…

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Q: Suppose A=[v_1...v_n]. Prove that if A(x)=b is consistent if and only if b is an element of…

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Q: The HAIR Company offers two brand of shampoo:Brand H and Brand S.There where 100 people who were…

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Q: 3) (i) Let X be a set containing elements a and b. Define T= {X, Ø, U| a E U and b E U}. This is a…

A: Definition:  A collection of subsets I of X is said to be a topology if it satisfies following…

Q: 2. Determine if the following vectors constitute a linearly independent set.

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Q: 2. Let Let T: VW be a linear map. Let {₁,..., Un} be a list of n vectors in V. Prove that if the…

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Q: 6. For A, B, subsets of R, define A+B= {a+b : a € A,b € B} and A·B = {ab : a € A, b E B} (a) For A =…

A: Answer: As per guidelines we can do only 3 subparts of question and the solution of this is given…