1. For A = 1 1 ] and x = [x₁ x₂]T E R², show that Vx (x¹ Ax) 2 Ax.

Q: -6x + 39y9z = -12 2x - 13y + 3z = 4

A: We have to determine the rank of the matrix.

Q: If f(x) is optimal at x = x*, show that the minimum of first even derivative of f(x) [i.e. f"(x)] at…

A: Stationary Points:A stationary point of a differentiable function f(x) is a point on the graph of…

Q: 2 2 All vectors (a, b) in R² such that a²=b².

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Q: For the following prime p and number a, compute a−1 mod p in two ways: (i) Use the extended…

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Q: Q6. Let A be the set {a, 3, 7, 6}. For each of the following relations on A, draw the arrow diagram…

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Q: Consider the set 2 C c = { 1 - ² / / n,m<N}. m Find, if they exist, inf C and sup C and prove your…

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Q: Answer T, ao = 2 3π an = f(x) = Jo if x = [-7,0) sin (3x) if x € [0 3(1 + (−1)n (n² - 9) T if n #3,…

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Q: Consider the sets A = {5n+3 | n ≤N}, B = {3n+2 | n ≤ N}. (a) List three elements in A. (b) List…

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Q: Q5. Solve the following initial value problem. (D³ + -2D²-9D + 181)y = e²2 y (0) = 4.5 y'(0) = 8.8…

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Q: Question 8 Travelling at 90 miles per hour, how far would you travel in 1 hour 40 minutes? 90 miles…

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Q: The matrices and vectors listed in Eq. (3) are used in several of the exercises that follow. A = C =…

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Q: Let f(w) = tr(Bww A), where A, B € Rn×n are squared matrices of size n × n, and tr(A) is the trace…

A: We have to find Δf(w)

Q: Find the kernel of the matrix [3 61 g] 8

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Q: Find the coefficients of the trigonometric, symmetric interval Fourier Series for the function:…

A: f(x) is periodic woth period 2π, piecewise continuous and integrable in [−π,π].The Fourier series of…

Q: If she all integ Then it is generated by an indegad ideal of of a sing Zl of s is maximal if and…

A: If S be an ideal ofg a ring Z of all integers. Then we have to show that S is maximal if and only if…

Q: Consider the differential equation for y(x): a) d'y dx² dy 4- da + 4y = 0. Consider the auxiliary…

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Q: Problem 2. Let p be a real number such that 1 0, and the function Tf is continuous on 10, ∞[ and…

A: Given information:Let us consider the given operator T,(Tf)(x)=1x∫0xf(t)dtTo prove:The operator T is…

Q: A fish tank initially contains 40 liters of pure water. Brine of constant, but unknown,…

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Q: The matrix model below describes the population of a plant species with three age classes (year year…

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Q: 2. Find a permutation matrix P so that PA = LU. A = 1 3 24 6 368 09 0

A: We have to find permutations matrix P If we have a square matrix A, then an upper triangular matrix…

Q: x + 2y = 6 3x + 5y = 20 -4x + y = -42

A: Given system of linear equations are  .a solution  of the given system means that it satisfies all…

Q: =t₁S = {3 +; = {3+1 ²+/2 = ne ¡:neN}. Prove that sup (S) = 4.

A: An element M is called an upper bound of a set S if there exists a number M such that for all..For…

Q: Exercise 4. Suppose f I→ X is a continuous map from the interval ICR to the topological space X.…

A: As per the question, we address three key propositions regarding a continuous map f:I→X from an…

Q: 1. Solve the differential equation using Frobenius Method 2x(1-x)y" +(5-7x)y' - 3y = 0.

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Q: If f is a homomorphism of a group G into a group G' with Kernal K. Let a € 6 be such that f(a) = a'…

A: We are given that f : G → G' is a homomorphism. Kernel of f is K.     =&gt; for all elements x in K,…

Q: 3. Recall that z = x+iy. For each of the given functions, use a result related to the Cauchy-…

A: Since you have posted a multi subparts question according to guidelines I will solve first(1,2,3)…

Q: Given that S be a proper ideal of a ring R. Then our claim is that S is contained in a maximal ideal…

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Q: Solve the following system of linear equations: 3x1+6x2-3x3 -2x1-4x2+2x3 2x1+4x2-2x3 = 8 = 12 -8 =…

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Q: Consider a random variable X with probability density function given by f(x) = 0.2 0.2x - 0.2 0 for…

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Q: 1. Prove that if we colour the edges of K5 with 2 colours, red and green, so that the number of red…

A: According to the question,contradiction. Suppose you color the edges of ​ (the complete graph on 5…

Q: Show that the system consisting of all elements of the form a+b√5, where a and b are any rational…

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Q: Exercise 1.8.2: Solve the following exact equations, implicit general solutions will suffice: b) x²…

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Q: (a) Prove that if the collection {A i E Z+} is increasing, then nA = A₁. ¡EZ*

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Q: how many student have seen none of these movies and how many have seen 2 or more?

A: Given that 18 had seen The Matrix(M)24 had seen Star Wars (SW)20 had seen Lord of the Rings (LotR)10…

Q: Limit calculations. For each real-valued sequence, explain whether it is convergent, divergent to…

A: The given sequences are,c) d) .We have to check the convergence of the sequence.

Q: 1. Solve the differential equation using Frobenius Method 2x(1-x)y"+(5-7x)y'-3y=0.

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Q: Which situation demonstrates the law of large numbers? If you roll a six-sided number cube 420…

A: In the given problem, we were asked to choose situation which describes the law of large numbers.

Q: (→ ≥ |ɛ − (x)ƒ|) v (g> |z - x|) xĒ SA ³E O ¿(³ > |ɛ − (x)ƒ |) ← (9> |z − x\) XA SE A following is…

A: When we negative a setence the following symbols changes as and the implication 'if  p then q'…

Q: 2. Let m, n, a, b € Z. Prove that if 6 | m and 6 | n then 3 | (am + bn +15).

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Q: -10 -8 6 A - Not 10 00 (O N -2 466 8 -10 2 4 6 8 10 0 -10 -8 6 10 8 6 4 4 2 10 -2 -4 -6 -8 -10 4 6 8…

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Q: Question: Use De Moivre theorem of complex number to find the constants P, Q and Rif sin² (0) cos³…

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Q: 4) If z is a function of x and y, what would its exact differential be?

A: is a function of  and .We have to find its exact differential

Q: A pension fund manager decides to invest a total of at most ​$35 million in U.S. Treasury bonds…

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Q: Find an LU-factorization of the following matrix by hand, showing all intermediate steps and row…

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Q: K The ratio of a quarterback's completed passes to attempted passes is 2 to 7. If he attempted 28…

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Q: The graph of f is given. State the numbers at which fis not differentiable. X = (smaller value)…

A: The function is not differentiable on following points1) the point at which the function is…

Q: Write 114+112 + 14 in base eleven. Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, T. The sum is eleven…

A: We all know that to convert from base 11 to base 10 we simply expand a number on the base of 11 as…

Q: A 20 kg mass stretches a large spring 10 cm in equilibrium. It is attached to a dashpot that…

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Q: "Determine the maximum and minimum values of the _ƒ(x, y) = −2y + 3x+2 on the closed bounded curve…

A: subject toAssumeLets use method of Lagrange Multipliers to solve it

Q: -5 -4 -3 -2 -1 5 4 3 2 1 -1 -2 -3 -4 -5 2 3

A: