Let A = [1,2,3,4; 0,0,1,-1; 2,0,0,-3;1,2,2,5] Determine the rank of A.

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: Determine whether the set in P_2 is linearly independent.    S={x^2 , +1, 2 - 1, 2}

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Q: Determine whether the given set is linearly dependent or linearly independent: S =

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Q: Let A=(1,2,3,4), B-(00,01,10,11), C=(x.y,z). f-(1,00),(2,01).(3,01).(3,10) (4,11)). f -((1,x),…

A: The question is based on composition of function  f: X→Z and g: Z→Y then gof: X→Yalso  gof(t) =…

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

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Q: Let a and b be integers, at least one of them not 0. Prove that an integer e can be expressed as a…

A: Let a and b be intgers ateast one of them not 0. Our Aim is to prove that an integer e can be…

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

A: The given relation is -2,5,-1,3,0,-1,1,-3,2,-5,3,-7

Q: Let R1 = {(1,1), (2,2)} and R2 = {(1,1), (1, 2)} be relations on A = {1,2}. Then R1 UR

A: In this question given that two sets R1 and R2 and we find the unions  of these sets and relation of…

Q: Let A=(1,2,3,4), B=(00,01,10,11), C=(x,y,z). f1 = {(1,00),(2,01),(3,01),(3,10) (4,11)}. %3D f2 =…

A: Given that:

Q: Which of the following sets is linearly independent in P2 ? {1+x + x?, x – x²,x + x²} the above set

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Q: Let A={1,2,3,4}, B={00,01,10,11}, C={x,y,z}. f1 = {(1,00),(2,01),(3,01),(3,10) (4,11)}- f2 = {(1,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: Let R = [1, 2] × [1, 2]. Compute ye*"dA. R

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Q: Which of the following sets is linearly independent

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Q: Q3) Determine whether the following set is linearly independent. (0,3, –3, –6), (–2,0,0, -6), (0,–4,…

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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: Let i = (– 3, - 2, 3) and i = (1, – 6, – 7). Compute the following: i xü = i x ủ u X u =

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Let

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Q: 9. Let 3 9. A = 2 0 and B = 1 2 1 -3 1 -7 -1 1 0 Find all r E (-0, 00) such that r(A) = r(B), where…

A: Solving

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: -目日日 1 Let 2 2 for which value of k, the set is linearly independent? k

A: See the attachment

Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A UB…

A: To evaluate the given set operations.

Q: Let A=(1,2,3,4}, B=(00,01,10,11}, C={x,y,z}. f = {(1,00),(2,01),(3,01),(3,10) (4,11)}. f2 = {(1,x),…

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Q: Represent the relations on {1, 2, 3, 4} with a matrix and digraphs.  (The rows and columns…

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Q: Let A = {x € Z*:x|12} and B = {x € Z*: 3|x}. List the elements of AOB.

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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: Determine whether the set S is linearly independent or linearly dependent. S = {(4, 0, 0), (0, 7,…

A: Linearly dependent.

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: Let R be the relation on the set {1, 2, 3, 4} containing the ordered pairs (1, 1), (1, 3), (1, 4),…

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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 A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using…

A: Given  A = {a, b, c, d} R = { (a, b), (b, c), (c, d), (d, b)}

Q: Determine whether the set S is linearly independent or linearly dependent. S = {(8, 0, 0), (0, 7,…

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Q: Determine whether the given set in R' is linearly independent or linearly dependent. a) {(1,-1,0),…

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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: Determine whether the set S is linearly independent or linearly dependent. S = {(3, 0, 0), (0, 9,…

A: Given: S=3,0,0,0,9,0,0,0,-14,3,5,-7 As dimℝ3=3 So, the set of 4 vectors in ℝ3 linearly dependent.…

Q: A.  Write the relation on {a, b, c, d} in matrix form. 1.  {(a, a), (a, d), (b, c), (c, d), (d, a),…

A: The matrix form of a relation is given by M=Mij , where Mij=1    if ai,bj∈R0    if ai,bj∉R Part(1)…

Q: Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find B U (AN C). || {

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Q: Let U={a,b,c,d,e,f.g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

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Q: Determine whether the set S is linearly independent or linearly dependent.S = {(−2, 1, 3), (2, 9,…

A: Consider the given set of vectors: Here the objective is to check whether the vectors are linearly…

Q: Determine whether the given set in R' is linearly independent or linearly dependent. a)…

A: b. The given set is                       -1,1,2, 0,2,-1, 3,1,2, -1,-1,1 A set of vectors v1, v2,…

Q: 1- Let X = {1,2,3,4,5}, A = {2,3,4} find A°, ext (A), and b(A).. = {X,Ø, {1}, {3,4}, {1,3,4},…

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Q: Let w = (2, − 1, 1), v = (− 4, − 5, 1), and u = (6, − 2, 2). Find u × (v × w)

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Q: Determine whether the set S is linearly independent or linearly dependent. S = {(7, 0, 0), (0, 9,…

A: Given the set S=(7,0,0),(0,9,0),(0,0,-8),(7,5,-4) We need to check whether the set S is linearly…

Q: Determine whether the following sets in R³ are linearly independent. a. S = 3 [8] 3 3 b. S =

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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: Determine whether the set S'is linearly independent or linearly independent. {(1, –4, 1) , (6, 3,…

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Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

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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.