find a control u(t)  for x`(t)=  [2, 1 ; 1, 1]  x(t) +  [1; 1] u(t),    x(0)= [5; 0]                                                             so that x(2) = [0; 0] .

Q: Prove that Ją (2) = =- J¼ (2) – J_4 (=)

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Q: 2. Consider the ARMA(1,1) process: xt = axt-1 + Wt + Bwt-1, where we is white noise. (a) Write an R…

A: In this problem, we are dealing with an ARMA(1,1) process, which is a combination of an…

Q: ppen inter

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Q: (a) Prove the set (A(*)./a(*),fa(a)) is linearly independent. (b) Use Gram-Schmit process to find an…

A: Given,     f1(x)=3,  f2(x)=1-x, and f3(x)=x2+2x-1

Q: Quest The moment generating function of X is given by Mx() = exp(2e - 2} and that of Y by Myt) = (e…

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Q: Let T: P3 → R³ be defined by T(ao + a₁ + a₂x² + ³x³) , and C= (18-8-8) Given [7] Pc (T(u)). = 4 1 -4…

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Q: Sketch the graph of f(x) if ...f'(x)>0 on (2,4) and f'(x)<0 on (−∞, 2) ∪ (4, ∞),f''(x)>0 on…

A: Here we suppose that the given function is continuous on the given intervals and differentiable on…

Q: Į c(x + y?) for 0 <x< l and 0 < y < 1, S(x, y) = otherwise. Determine (a) the conditional p.d.f. of…

A: The required pdf is given by: fy=∫01fx,ydx=∫01cx+y2dx=c∫01xdx+∫01y2dx=cx22+xy201=c12+y2

Q: Let f(x) = ax + b/x. What are the critical points of f(x)? i

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Q: Let Y = Σ(Xi-X)² ~ X² (n-1) Using the TRANSFORMATION THEORY Find the distribution of S²= E(Xi-X)²…

A: Given Information: Consider  Y=∑Xi-X¯2σ2~χn-12

Q: Find continuous functions f1, f2, f3, f4 defined on the open unit interval I = (0, 1) (i.e.…

A: 1. f1(x) = (M1 - L1)x + L1, for all x in (0, 1)  This function is linear and maps (0, 1) onto (L1,…

Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: Define briefly u(t) and 8(t)

A: u(t): u(t) represents the unit step function, which is defined as u(t) = 0 for t &lt; 0 and u(t) = 1…

Q: Orthonormalize [1, t, t²} in P₂(R) with (p, q) = p(0)q(0) + p(1)q(1) +p(2)q(2) }

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Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: Exercise 2. Show that if u(x, t) = F(x+ct) +G(x- ct) satisfies u(x,0) = f(x), u(x,0) = g(x), for all…

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Q: Find f(2021) if function f satisfies following conditions: f(1)=1, f(x+y)=f(x)+f(y), for all x,y…

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Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: Let a(t), 2 < t< 8 be a positive function. Also, let the function 8(t) be defined as a'(t)/a(t) on…

A: We will find out the required expression.

Q: 1. (a) Derive the autocovariance for y; in the following MA(3) model and explain why the MA model is…

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Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

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Q: The Boolean function F(x, y) = x'y + xy' + (x+y')x can be simplified to:

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Q: Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2,…

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Q: Example 1.5. Let X = R? x R² and d1 : X R, such that, (1) di(x, y) = d;((r1, 12), (Y1, Y2)) =| ¤1 –…

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Q: Prove that • I %3D

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Q: Let the function ƒ : {1,2, 3,4, 5} {1,2,3, 4, 5} given by the following table. 1 2 3 4 5 f(x) | 4 1…

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Q: 6) (1+x)у" + (4x+5)у + (4x+6)у %3 е2х a special differential equation solution y1 e-2x Find the…

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Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: 1 1 -dt 4 W (t+1)* (t-1)* 4 (t+1)ª

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Q: -> Let q: XS¹ be a continuous map where X is simply connected and let i: S¹ S¹ be the identity map.…

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Q: If the invertible function f (x) satisfies f (12) = 6, then which of the following statements is…

A: Option C is correct option.

Q: 3. Find f. (g) f'(x) = 2x – e

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Q: the book is "First Course on Fuzzy Theory and Applications"

A: To calculate the fuzzy definite integral with the given data