Find the dimension of the set S= {(2, 4), (4, 8)}?

Q: Which of the followwing sets is linearly independent? O M={ (1,1,3),(3,2,0), (4,5,6)} O…

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Q: {k}, {I, m, o}, {n, p}} of the set U = {k, I, m, n, o, p}. Give the

A: Solution is attached below.

Q: Determine whether the set S is linearly independent or linearly dependent.S = {(4, 1, 2, 3), (3, 2,…

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Q: List all of the subsets of (x, y, z).

A: Given that the set x,y,z. Find all the subsets of the given set. Definition: A set is a well-defined…

Q: Let १ १G,१ी, (३,5) , (3 ), (4,2 ), ( 3 4) 5 %3D and 4. १,०) (2) (৬,), (,০), (3,) 3 %3D which of the…

A: The solution of the problem is given in the next step.

Q: 2.44 Show that if a vector is in the span of a set then adding that vector to the set won't make the…

A: The given statement is " if a vector is in the spanning set then adding that vector to the set would…

Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one %3D such. If not, Why not exactly?

A: No, A≠{A} for any set A. Let  A=1,2,3 then number of elements in A are 3. Now,  A=1,2,3 here the…

Q: Determine whether the points are coplanar.(1, −5, 9), (−1, −5, 9), (1, −5, −9), (−1, −5, −9)

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Q: Suppose that N+ 1 balls, of which a+b+1 are red and N-a-bare blue, are arranged in a linear order in…

A: From the given information, There are N+1 balls, of which a+b+1 are red and N-a-b are blue arranged…

Q: Show the span {(1,0, 1), (-1, 2, 3), (0, 1, – 1)} is all of R'.

A: Let x=1, 0, 1, y=-1, 2, 3 and z=0, 1, -1. We have to show that spanx, y, z is actually the vector…

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: determine whether set s={(2,1),(-1,2)} spans R^2

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Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

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Q: List all subsets of the given set. (α, β, Γ, Δ}

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Q: Is the set X is linearly dependent or independent X = {(1,0,1,0), (0,3,0,1), (1,1,2,2), (3,4,1, −2)}

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Q: Find the value of t for which (4, 6, 3, t) belongs to Span {(1, 3, -4, 1), (2, 8, -5, -1), (-1,…

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Q: Find the union of the sets. {e, m, p, t, y}∪∅

A: we have to find the union of the sets. e,m,p,t,y∪∅

Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover?

A: This is the question of Topology.

Q: Let (X, M, u) be a measure space wE

A: Given, (X, Μ, μ) be a measure space where μ is a probability measure. Assume thatf, g : X→ℝ are…

Q: By inspection, determine if each of the sets is linea (a) S= {(1, -2), (2, 3), (-2, 4)} O linearly…

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Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: Find all (a, b, c, d) in R* such that the given set is orthogonal. What is the value for a? {(1, 2,…

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Q: 10 What are the coordinates of the point on the directed line segment from K(-5,-4) to L(5, 1) that…

A: Use mid section formula for evaluating the coordinates of points.

Q: The vectors {x+1,x2+x+1,x2+2x+1}{x+1,x2+x+1,x2+2x+1} form a spanning set for P3P3.

A: Given the set of vectors,      (  x+1 , x^2+x+1 , x^2+2x+1 )

Q: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

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Q: Does the set S = {(1,2, 3), (0, 1, 2), (-2,0, 1)}span R³? %3D O Yes O No

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Q: ) Suppose X = {1,2, 3} and Y = {5,6). The number of elements of the set P(X × Y) = %3D

A: Number of Elements in Power Set P(A) of set A with n elements is 2n

Q: Let à = (1, 1, 4) and b = (1, 2, - 5). of b onto a. - Find the projection proj- 6 = b =< -

A: For the given vectors the projection of b on a is given by

Q: Determine if the set is linearly independent. S = {(4,0,1), (0, -3,2), (5,10,0)}

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Q: Use Venn Diagrams to find A \ B and B \ A where A = {1,2,3} and B = {2,3,4}

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Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

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Q: find the complement of set B, given that U= {x ∈ z/ - 7 < x < 7}     A= {x ∈ z+ /2 < x < 6}     B=…

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Q: The vectors {x+1,x2+x+1,x2+2x+1} form a spanning set for P3

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Q: Prove using Venn diagram that An (B U C) = (A n B) U (A n C)

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Q: find the subset of (E, B,T,*)

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Q: Suppose Ak,., A2 , A1 and B are points on R" Prove that if {A1 , A2, .. Ak} is an independent linear…

A: proof :- A1,A2,...Ak are linear independent set ⇒c1A1+c2A2,...ckAk=0  where c1=c2=...=ck=0…

Q: - Consider noncoplanar points A, B, C, and D. Using three points at a time (such as A, B, and C),…

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Q: Find the union of the sets {a, e, i, o, u} ∪ ∅

A: Given: The set {a, e, i, o, u} and ∅ function. {a, e, i, o, u} ∪ ∅ To find: The union of the set.

Q: Match the following sets with their cardinalities. {t, 5, 1, p} Choose... {0} Choose... Choose... {}…

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Q: Let F(x, y, z) = (z, x, y), ar (0,0,0), (0, 1, 1), vertices are ar

A: Introduction: Stroke's theorem is simply a higher-dimensional version of Green's theorem. The line…

Q: Suppose {u,..., 4,, W1, ..., W,} is a linearly independent subset of V. Show that span (u;)…

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Q: 2 Find values for a, b, and c such that is an orthogonal set.

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Q: Explain why the set is not a Basis. S = {(2,3), (6,9)}

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Q: Find the set A UØ. U= {1, 2, 3, 4, 5, 6} A=(3, 4, 5, 6}

A: Given, U=1, 2, 3, 4, 5, 6, A=3, 4, 5, 6

Q: Find n(A) for the set. A = {300, 301, 302, ..., 3000} %3D

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Q: Let ä = (4, – 4, 0) and b = (- 1, 2, - 4). Find the projection of b onto a. proj, b = <

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.