3. Given 1 1 -j -1 j A = 2 1 -1 -1 -1 -j] where j= -I. (a) Calculate |||1, || 4||2, and ||||p. (b) Show that for any z E C, it holds ||Ar||2 = |r||2. 1. 112

Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: 6.8. Suppose the cubic spline s E S3(N3) is such that s(x) = 0 for x E [xo, x1] and for xe[x2, x3].…

A: Given: The cubic spline s∈S3Ω3 sx=0 for x∈x0,x1 and for x∈x2,x3   To show: sx=0 for x∈x1,x2 (a.) by…

Q: 19. Let a, = (-1)" Vn 2 1. Calculate the value of an+1 - a, for odd values of n. %3D А. -1 В. -2 С.…

A: As this is a multiple question type, according to Bartleby Answer Rule, only 1st question is to be…

Q: Find the value(s) of k such that A is singular.

A: The given matrix will be singular if the determinant of it is 0

Q: 3 x 3 boyutlu A bir matrisi aşağıdaki denklemleri sağlasın: A 2 = A 3 = 3 A 0 = 0 To o 1° P = |0 1 1…

A:

Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: x2+1 =0 Has soluion in R

A: Solution:

Q: 2 1. Given: h (t) = : ; Find h'(t). On (t) = 8t° (1+t²) (1²+2)³ 8° (t² –1) (1²+2)° ON (t)* O (t)…

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Q: If z + In(e 2 – e" + e*) = 0 -2x az find at the point (0, 0) O-3 O 3 O-2 O 2

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Q: 5. Use Taylor's theorem to write down an explicit formula for R, (1). Conclude that R, (1) + 0, and…

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Q: 4. Define f: [0, 1] → R by if x E Qn [0, 1] if x ¢ Qn [0, 1] f(x) = (a) Prove that S° f = 0; s*f =…

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Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: 1E(X; – Xn)². Prove 1. Let X1,..., Xm,... - iid N(u, T) and consider the MLE în that î, is a…

A: Given X1, X2, … Xn iid N(µ, τ) Given MLE

Q: (a) Let a > 0. Using the substitution t = In x or otherwise, prove that In a e 4/a² - e 2t dt =a5…

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Q: 7. Let Te L(V, V). Prove that T2 = 0 if and only if T(V) c n(T). %3!

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Q: 23. If u = f(x), then +2x² + 1 k + C for some constant k . x² + 1 Compute kf (1). (a) ¼ (b) – ½ (c)…

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Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: 9. Verify that p(t) = te/50 satisfies the condition p(t) dt = 1

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Q: 8 1 ₁ }(s) = = nº n=1 Show that finding the value of the Reiman Zeta for (2) is just the value Basel…

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Q: S 1.Prove that L (coswt): %| s2 +w2

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Q: (6) Let x1, -- ,X1o N(u, o2), where µ e R and o > 0 are unknown parameters. Consider the following…

A:

Q: Suppose that F(s) = ℒ{f(t)} exists for s > a ≥ 0. Show that if k is a positive constant, then…

A:

Q: 84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

A: Answer (a): To prove : ex≥1+x if x≥0 The given inequality can also be written as: ex≥1+xex-1-x≥0

Q: 10.Show that Φ(t) = Ψ(t)Ψ−1(t0), where Φ(t) and Ψ(t) are as defined in this section.

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Q: Σ (-1)" Given: sin x = .2n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: Sum of the series, using Taylor series expansion

Q: 2 Let xk = E(k+1)(k+2) for all k e N and define S, = Ek=1 ®k• (a) Evaluate Sn as a function of n.

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Q: Show that g(t) = t2tant takes on the value ½ for some t in [ 0 , π/4 ].

A: gt=t2tant on the interval 0, π4. When t=0, g0=02tan0=0 When t=π4, gπ4=π42tanπ4=π2161=π216=0.6168

Q: 6.Suppose that the joint p.m. f. of X and Y is X- 00 Yə -1- 09 10 Determine: (1)-The value of a;…

A: Given:     x y   0 1 2 -1 0.05 0.1 0.1 0 0.1 0.2 0.1 1 a 0.2 0.05

Q: 1.4 For which values of a eR is the function ar? f(x + iy) = (a'x – axy) +i (- + ay an entire…

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Q: 1.1 Solve for x in cach of the following: 1.1.1 * +x-12=0 1.1.2 V2x+1 =x-1 1.1.3 2 = 27 1.1.4 x…

A: As per the guidelines we are allowed to solve one question. So please upload the other questions…

Q: 4. Prove that if f(x) = agx" + a,x"-1 +..+ an-1x = 0 has a positive root x = xo, then the equation…

A: Note that f0=0 and that fx0=0. So using mean value theorem there must be some 0<λ<x0:…

Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: 6) In the process of calculating 7s + a In 7s + b L Where a and b are constant, it is obtained that:…

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Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0. {e' cos 2t, e' sin 2t}…

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Q: 3 (5) Suppose that T : R³ → R² „such that 2 1 1 T (e,) = T(e.) T(e,) = and T (e,) = 1 1 3 2 T Find -…

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Q: (-1)" p2n+1 (2n+1)! Given: sin x for x E R n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact value of…

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Q: 1. Given that X1 = 1 X4 =-2 Xs = 4 X6 =-1 X7 = 5 X2 = 3 X3 =0 Xg = 2 X9 = 10 %3D Γind (a) E X;, (b)…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Prove that (À × B) · (B x T) × (T x A) = [ABT)

A: The objective is to prove that

Q: 1 3 3. Use the IVT to prove that y = x ln x has at least one zero on 2' 2

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Q: 8. Let 2ni S7 = e7 = cos- 27 + isin- 7 7 a. Prove that E¢ = 0 k=0

A: we have ζ7=e2πi7=cos2π7+isin2π7we have to prove…

Q: 18. (2) = t"(-t)" dt, show that F(m). m! +1, n+1 %3D m and n are positive integers.

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Q: For the following PMFS X and Y for k e {0,1,2,3, ..] Px (k) = { %3D otherwise for k e {0,1,2,3, ...}…

A: From the given information, PXk=e-λλkk!, k=0,1,2,3,....PYk=e-λλkk!, k=0,1,2,3,.... If λ=1, a) The…

Q: Theorem 8.3.3 If X ~ t(k), then E(X2r + 1) = 0 and µz, = k"- (2r – 1)(2r – 3) ... .1_ (k– 2)(k – 4).…

A: Answer: For the given theorem, The proof is:

Q: 1.1. Show that Y(n) max(Y1, Y2, ..., Yn) is sufficient for 0.

A:

Q: 1. (a) Suppose that x1 = -5, x2 = 36, x3 = Calculate the following quantities: 4, and y1 = -7, y2 =…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 14. Substituting appropriate values for x and y into the formula of Theorem 9, show that (a) = 2";…

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Q: x+1 Q1/ Prove that coth-1x = x-

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Q: 9. Suppose that N(h) is an approximation to M for every h > 0 and that M = N (h) + K,h+ K,h? + K3h…

A:

Q: 2)The critical number/numbers of f(x) = tan(x? – 1) is/are A)0,1 B) 0 C)T, 2n D)2n,1

A: Given fx=tanx2-1