[k 0] [1 0] or k 0. 1. k] or [0 1] k 1

Q: -2x Use Green's Theorem to evaluate [(3 ye^²* − 7 sin² (3x³)) dx + (5x² + 2x²y² +8e³¹²-7x+²) +2) dy…

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Q: Calculate the following limits, or explain why they diverge. (d) lim sin n→∞ (e) lim n→∞ n+ 1 n² + 1…

A: Limit of the sequence

Q: 1) Solve the following ODE using the power series method y" + sin(x) y' + cos(x) y = 0 i)

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Q: 2. Let A 0 1 0 0 0 1 2 -5 4. Is A diagonalisable? If so, find a basis for M2,1 (C) consisting of…

A: It is given that the characteristic polynomial of the matrix A is cpAx=x-12x-2. We have to check…

Q: Let L₁ be the line passing through the point P₁(-3, 1, -2) with direction vector d=[0, -1, 2]T, and…

A: Expressing the equation of lines in vector form.

Q: 2. Sketch the graph of a continuous function f(x) with domain [-1, 8] which is differentiable on…

A: There is continuous function f(x) whose domain is [-1,8] and differentiable on -1,8, which…

Q: Subgroup H of a group G is a normal subgroup of G if and only if the product of two right cosets of…

A: Let H Be a normal subgroup of a group G, and x,y be any two elements of G. Hx ,Hy are any right…

Q: Four partners are dividing a piece of land that each see as worth $124,000 among themselves. They…

A: Four partners are dividing a piece of land that each see as worth $1,24,000 among themselves. They…

Q: Use the definitions of sin(z) and cos(z) T 2 prove that sin z+ = cos(z) for all z E C. (Do not use…

A: Answer :-

Q: Find a non-zero vector in Nul A and a non-zero vector in Col A for the following matrix: 1 2 4 5 -5…

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Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

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Q: if sis a group of order p", then its center 24, peing a primes

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Q: (a) 64x 56 (mod 52) (b) 14x = 35 (mod 56)

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Q: value 1. Let K be the subgroup of positive real numbers. Determine whether or not he canonical map H…

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Q: Use finite difference to determine the equation for the polynomial corresponding to the table of…

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Q: Assume that 0 0, consider the sequence of sets: A₁ = {\fn-f|> }, n=1,2,... (1) Show that, for every…

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Q: Prove that for any graph G, y(G) ≤ 2ir(G)-1.

A: Please find the attached solution

Q: Define f: [1,00)→ R by f(x) = (-1)"/n for all z € [n, n+1). Prove that (a) f exists; (b) f is not…

A: Please find the attached solution

Q: In which option can you find a linear independent set of vectors? {(1, 1, 1), (0, 0, 0)} {(1, 0, 0),…

A: As per our guidelines we can answer only first three subparts and rest can be reposted. Linear…

Q: The limit of the function f as x approaches a is the number L, written as limx→af(x) = L, if for…

A: We have to show that limx→1+ 41-x=-∞ i.e., the function fx=41-x approaches infinity when the…

Q: Count and describe the subgroups of index 3 of the group Z+ × Z+.

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Q: If V is the volume of the solid obtained by rotating the region under the curve y cos(x) from x-0 to…

A: We will be using cylindrical shell method Volume (V) of the region formed by rotating the region…

Q: 2.15 Find a graph G with 10 vertices, 24 edges and Y(G) = 4. 10 2193

A: Please find the attached solution

Q: Chapter 6, exercise 4.2(b): List the proper normal subgroups N of the dihedral group D₁ and identify…

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Q: rotate the vector v = The rotation matrix R = H IT by an angle of in the CLOCKWISE direction. The…

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Q: (b) Let G=(Z8, +) and f: GG be defined by f(x) = 2x and show that f is a homomorphism that is…

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Q: Problem No. 1. Three products are made by the Wright Company. The contribution of each of these is…

A: Max Z=2x1+4x2+3x3 subjected to 3x1+4x2+2x3≤602x1+x2+2x3≤40x1+3x2+2x3≤80 The problem is converted to…

Q: Let ux,t=XxYy Given…

A: Note: As per your requirement I answered here on papar.   The required answer is in below step.

Q: C. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the…

A: Sequence: A sequence is defined as the list of numbers that form a pattern.

Q: (b) Let B={(0,2,-2), (1,0,-2)} be a basis for a subspace of R³, and let x = (-1,4,-2) be a vector in…

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Q: S(1) = 5; S(2) = 11; S(n) = 5S(n − 1) - 65(n − 2) for n ≥ 3. S(1) = 3; S(2) = 14; S(n) = 4S (n − 1)…

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Q: |x|· x x+0+ x² (a) lim x² xxx + √√3x + 1 x² - 10x (d) lim Calculate the following limits, or explain…

A: To Find: Limits ( And explain if it is divergent). (a) limx→0+|x|·xx2 (b) limx→∞x2x+3x4+1. (c)…

Q: er indi (a) (3,5) U {6} (b) (-∞,0) U (0, 1) (c) {1, 2, 3, 4, 5, 6, 7, 8, 9) (d) (-∞, 0) U [0, 1) (e)…

A: “Since you have posted multiple questions with multiple sub parts,we will provide the solution only…

Q: Given that P(E) = 1.8, what must be true about the event E? Select the best answer. This is not a…

A: I have given the answer in the next step. Hope you understand that

Q: Express answer in standard form [(5 + 2i)(−1+ 4i) - 5260°]*

A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

Q: 6 Q3. Evaluate Σή=1 5n2 - 7n.

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Q: (d) Let G be a group, N a normal subgroup of G and K a subgroup of G which contains N. Then prove…

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Q: The given table indicates the transactions for one teller for one day. Find the probability that a…

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Q: 22. The sum of the measures of the interior angles on the drawing of the site plan below equals D in…

A: We know that the sum of interior angles of a polygon is ( n − 2 ) × 180°. where n is the number of…

Q: Calculate the following limits, or explain why they diverge. 3n²+ n-1 n→∞ -2n² + n-4 (a) lim

A: Limits of the rational sequence

Q: a = 3 iff N(a) = G. also show that if G is finite, then a € 3 iff o(N E

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Q: x+z = hz 11p> to * Y (1) = 0

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Q: please do question 9 pleaase

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: (c) Let G be a group and a, b € G be elements of G each of order 3 such that a² = 6² and prove tha a…

A: Given: A group G, and a,b∈G order of a and b is 3 and a2=b2. To Prove: a=b.

Q: Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable…

A: please find the attached solution

Q: a. Given that 22³ ... 3z + 1 can be expressed in the form Ax (x²+1) + Br+ C, find the values of the…

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Q: Solve the Goursat problem:    Utt − c 2Uxx = 0 u|x−ct=0 = x 2 u|x+ct=0 = x 4 . Hint: Use the…

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Q: (a) Show that a ring with identity has only one identity element

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Q: ]i+ 5x sec² (xy) —- 3] + [6 y j+(6xz+2) e³x² –3]k, For F(x, y, z)=[5ysec²(xy)+6z²e³² find the curl…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 4x + 4y +3z, subject…

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