If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the reflexive closure of R? O {(1, 2), (2, 1), (1, 4), (4, 1), (2, 3), (3, 2), (3, 1), (1, 3), (4, 2), (2, 4)} O {(1, 1), (1, 2), (1, 4), (2, 2), (2, 3), (3, 1), (3, 3), (4, 2), (4, 4)}

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: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

Q: Let A = {1, 2, 3, 4, 5}. Define the following relations on A. R1 = {(1,1), (1,2), (2,1), (3,2),…

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Q: R, S, and T are relations defined on A {0, 1, 2, 3}. Let S = {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

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Q: Define relations S and R on the set A = {x, y, z, w} as follows S = {(y, x), (x, w), (w, z), (x,…

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Q: Let B = {0, 1, 2, 3} and the relations R, S, and T on Z are as follows: R = {(0, 1), (1,1), (2,…

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Q: Determine whether the set S is linearly independent or linearly dependent. S = {(8, 0, 0), (0, 6,…

A: Given,  S={(8,0,0),(0,6,0),(0,0,-14),(8,5,-7)}

Q: Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)}…

A: we have given relations R and S on {a, b, c, d} and we need to find composition R∘S

Q: Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 =…

A: “Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 =…

A: This is a problem of relation.

Q: 4. Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)), and let S be the relation {(2,…

A: To find the composition of two relations R and S . the domain of S°R will be same as domain of R…

Q: Which of these relations on {0, 1, 2, 3} are ?equivalence relations a) {(0, 0), (1, 1), (2, 2), (3,…

A: Given set = {0,1,2,3} As equivalence relation is reflexive, symmetric and transitive

Q: Exercise 5.2.1: Here are two relations: R(A, B): {(0,1), (2,3), (0,1), (2,4), (3,4)} S(B,C): {(0,1),…

A: Given: a. Compute πA+B, A2, B2R A B A+B A2 B2 0 1 1 0 1 2 3 5 4 9 0 1 1 0 1 2 4 6 4 16…

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

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Q: Let A = {2, y, 6} and B = {x, 4, z}. which of the following are relation from B into A O a. R = {(2,…

A: We have to find that relation

Q: Let

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Q: Let a=⟨−3,−2,2⟩ and b=⟨−4,−2,0⟩ Compute:

A: Given that          a = <-3, -2, 2 >    and    b = <-4, -2, 0> Here we have to compute…

Q: Let A={1,5,6,8,10} and R={(1,1), (5,5), (8,8), (10,10),

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Q: Let W1=span{(1,1,0),(-1,1,0)} and W2=span{(1,0,2),(-1,0,4)} Proove W1+W2=R^3

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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: Let S = {0, 1, 2, 3} and the relations A, B, and C on S are as follows: А %3 (0, 0), (0, 1), (0, 3),…

A: Equivalence Relation An equivalence relation on a set S is a subset of SXS, i.e., a collection  of…

Q: Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}

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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: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

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: Let A=(1,2,3,4), B={00,01,10,11), C=(xy.z). f, = ((1,00),(2,01).(3,01).(3,10) (4.11). %3D f2 3…

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Q: Let U = {1, (2), 3, (1, 2), 4). Let A = {1, (2), 3), B = {(2), 3, (1, 2), 4) and C = {{2}, 1, 4).…

A: A function is a relation where any element of the domain is mapped to at most one element in the…

Q: Is the set {(-3,0,3),(1,-1,2)(4,-2,2), (2,1,3)} of R' linear dependent over R?

A: Clearly dimension of R3 is equal to 3. So at max. we can have 3 independent sets. But here there are…

Q: Which is the inverse of the relation {(-2,5), (-1,3), (0,-1), (1,-3), (2,-5), (3,-7)}? O {(5.-2).…

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Q: Which of these relations on {O, 1, 2, 3} are ?equivalence relations а) (0, 0), (1, 1), (2, 2), (3,…

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Q: Which functions on {1, 2, 3, 4} x {a, b, c} is NOT onto? О {1, с). (2, а). (3, b). (4, b)} О {(1,…

A: Given sets are {1,2,3,4} and {a,b,c}. We know that a function f from A to B is called onto if for…

Q: Let S = {1,2,3, 4}. For each of the following relations on S give its transitive closure. a) {(1,1),…

A: Concept: In mathematics, the transitive closure of a binary relation R on set X is the smallest…

Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…

A: We have to Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as…

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

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Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Which of these relations on (0, 1, 2, 3} are equivalence relations? o {(0, 0), (0, 1). (0, 2), (1,…

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Q: Represent the following relation {1,2, 3, 4} with a matrix. {(1,1), (1, 4), (2, 2), (3, 3), (4, 1)}

A: Given below the detailed solution

Q: Let S = (0, 1, 2, 3} and the relations A, B, and C on S are as follows: %3D A = {(0, 0), (0, 1), (0,…

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Q: Show that the relation R in the set {1,2,3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is…

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Q: R = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6 e (yes or no) whether R has…

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Q: One of the followin relations is not symmetric,where A={1,2,3,4}: .a…

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Q: Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A=(1,2,3}.…

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Q: 2. Let X = {a,b, c, d, e, ƒ} and S be the relation on X defined by S = {(a, a), (a, b), (a, c), (a,…

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Q: If R = {(1, 2), (1, 4), (2, 3), (3, 1), (4, 2)}, what is the symmetric closure of R? %3D О (1, 2),…

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Q: 38. Let u₁ = (2, 1, -1), u₂ = (3,-4, 2), and u3 = (2,7, a). Find all values of a such that {u₁, U2,…

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Q: Let S = (0, 1, 2, 3} and the relations A, B, and C on S are as follows: A = {(0, 0), (0, 1), (0, 3),…

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Q: Which of these relations on {0, 1, 2, 3} are * ?equivalence relations а) ((0, 0), (1, 1), (2, 2),…

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Q: The symmetric closure of R is: Seç. Seç. {(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3). {(0, 1),…

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Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4

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

A:

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.