using Cayley - hamilton theorem [1 2 3 Let A = 1 2 Find A5. 0 1 2

Q: (3,7.148), (5,10.231). (8. 13.509), (12, 16.434) uct the Least square quadratic approximation to the…

A: Solution

Q: A. State De Moivre's theorem and if z 7+ j4, find z using the theorem.

A: De Moivre's theorem states that: cosθ+isinθn=cosnθ+isinnθ for all integers n. Also, it extends to:…

Q: -1 0 1 1 x+1 х Q1. a) Let A = 1 x € R. What is the rank of A dependent of x € R. х -1 1 х*+1 х

A: The given matrix is ,

Q: Linear Algebra Let T:RニR leiear tranaformatin be T(x)= Ax such thwet A = 2 - 1 is T: transfromatin…

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Q: Exercise 195 Further problems on Leibniz's theorem 7. Given 2x2y" + xy' +3y 0 show that 2x2 y(n+2) +…

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Q: =: (1)6 In(t)dt, 1, = e.

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Q: f(X1,X2)= f(X,).f (X2) If X,~N(H1,0) X2~N (H2,0) are not independent then ylgn ihi

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 0 1 0 0 0 0 Let A = 1 Then null(A) is and im(A) is

A: Ans:-   Let  A=010001000    we have to find Null A   &  im A

Q: (a) Let g(x) = x3, and classify each of the following as positive, negative, or zero.

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Q: 1 -2 1 2 Let A= 1 -1 -4 -2 5 1 (a) Find det(A). (b) Is A singular? Justify.

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Q: 3 0 Let A = and define T: R2 R by T(x) = Ax. Find the images under T of u = a and v = b. 0 3 -3 T(u)…

A: The detailed solution is as follows below:

Q: 1). Let, 2=x+iy *,y€R. In this case, (a). Prove the equations 2-2+2 and a = i.2 %3D %3D

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Q: W Let z = x₁ + iy₁ and w = x2 + iy2. Prove = e²-w ew

A: ex × ey  = ex+y  e-x = 1/ex

Q: 3.2 † Prove part (ii) of Theorem 3.1.2. Theorem 3.1.2 Let f and g be in R[a, 6} and c e R. Then i.…

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Q: 1+a 1 uestion 4. Let A = 1+3 1 1 1 1+Y such that a, B and y are all non-zero constants. Show that…

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Q: a O s(x) = a (x - b) o s(x) = %3D a o s(x) = (x- 6) (x - c) %3D %3D 00 a (x – b) (x - c) (x – d) a…

A: A small exercise to get the concept: Now look at the graph you cannot find the value of f(x) at…

Q: = -2 + 11i, z2 = 2 – i. Showing the details of %3| | your work, find, in the form x + iy: Re (z).…

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Q: Find the particular solution that satisfies the initial conditic (e* + eX), f(0) = 1, f'(0) = 0 2…

A: Here we have to find the particular solution of given differential equation.

Q: Evaluate f Z-1 č (Z+))(7-2) cîg the ciocle, 17-91=2. DO the where 8. %3D problem by cauchy's…

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Q: Using Variation of Parameters compute the Wronskian of the following equation. y" – 2y' +1 = (x+…

A: we have to find the wronskian using variation of parameters

Q: Duplicating the method of proof of Theorem 10,show that P(A∩B∩C∩D) = P(A)·P(B|A)·P(C|A∩B)·P(D|A ∩ B…

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Q: a) Use the method of Fredholm resolvent kernel to solve the Fredholm equation of the second kind,…

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Q: Exercise 2. * Let f(z) sin(3z) z²(z-n) and C: |z – 9| = 1. Then f. f(z)dz = а. 0 b. 2ni с. 9 d. None…

A: Singular point are 0 and π which does not lies in C

Q: show ALL WORK (calculus III) 1. Given a=4i – 3j+2K and b = 2;-4K find... %3D a) atb b) ya+2b c) lal…

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Q: 6: Let X ~ B(3,0) that is f(r; 8) = (C)0*(1 – 0)3-1,I = 0, 1, 2, 3; 0 < 0 < 1- %3D Let Ho: 0 = and…

A: Here, X ~ B(3, theta) Answer is given using concept of BCR. please find step by step solution below:

Q: Exercise 4. * Let f(z) = sin(3z) and C: |z| = 1. Then fe f(z)dz = a. 0 b. 3ni c. -6ni d. None of the…

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Q: 0 0 51 Let C =0 3 0 l2 0 ol 1. Is C diagonal? If no, diagonalize C using the spectral theorem of…

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Q: lim (t i − 4 j + t² k) 1-9 ■im (t i − 4 j + t² k) = i →9 i+ i

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Q: 3. (1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to Band g(x) = x from B…

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Q: 3. Let V = 6xy?z³ + 5 In(x² + y? + 3z²)V in free space. Evaluate each of the following quantities at…

A: Note: according to our guidelines we can answer only first three subparts

Q: letfeRiemann La.bT and dE Rieman. then AFERiemann [q.b] Showthat Sraf)(x) dX Riemann in tegkal)

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Q: True or false? If det(A)= 0, then A is not invertible.

A: Explanation: Case 1: If det(A) is invertible. In this case, det(A) not equal to 0 because in matrix…

Q: (2) Let x1, X2 - Xn uª N(4, o2). Find the MLE of ø = (µ, o2), when the parameter space is -o 0. iid…

A: Solution

Q: 3 0 3 and define T: R²→R? by T(x) = Ax. Find the images under T of u = - 5 a and v = b Let A = 0 3…

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Q: A Test the analy Hciby f the following functrons f(z)= z² f(2).= ē? 19-25t,ZE = (2)

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Q: Equational style proof of the following Prove A v ¬AT

A: If we consider  the truth value of A is False then ¬A has the truth value is True so we can conclude…

Q: 3 0 3 and define T:R²→R² by T(x) = Ax. Find the images under T of u = a and v = b Let A = 0 3 - 7…

A: Explanation of the solution is given below...

Q: Exercise 16. 12 Let C: |z |=1 and I = f. dz. Then a. I- πί b. I=0 c. I=-ni d. None of these

A: Given below the detailed solution

Q: ii. Prove the second translation theorem (in time): If F(s) = L(f(t)), then L(ua(t)f(t – a)) = e-a®…

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Q: az and ди az Q3. Evaluate at given point (u,v), z = 4e*lny, x = Inu cosv, dv y = usinv at point(u,v)…

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Q: -15 10] 4 -1 8. 10 2.

A: Solution is given below:

Q: f(2) = 1,f'(2) > 0, and f"(2) (а) 2+ 1 Derivay 1 the The the der (b) A Y dec 2 by thelsig Aeral char…

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Q: 26: Let X B(3,0) that is f(r; 8) C)0* . (1 – 0)3-,1 0, 1,2,3;0 < 0 < 1. %3D Let Ho 0 and H 0 =!.…

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Q: 1 2 1 0 Find a mat rixP such that P- 0 3 0 3 1 | OA. 0 1 1 1 P O B. %3D 0 1 1 0 %3D C. 1 1 1 0 %3D…

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Q: 5) Find f(25) given f(20) = 14, f(24) = 32, f(28) = 35, f(32) = 40, using Gauss's formula. %3D %3D…

A: Note:- In this problem, any particular type (Forward or backward) of Gauss formula is not mentioned.…

Q: The function f(x)= V(e 1)(3 x) satisfies the hypothesis of Rolle's Theorem on 1,3 [1, 3].

A: Three conditions for a function to satisfy Rolle's hypothesis within the interval [a, b] are: The…

Q: 1 0 1 0 Find a mat rix P such that P- 2 3 P= 1 -1 P O A. 1 1 0 1 %3D В. 1 0 С. -1 1 1 0 P. O D. %3D…

A: Let matrix P is                                                                  P=abcd given that…

Q: orm of the operator A(x) = So (s3 + s² )æ(t)dt, where A : C[0, 1] → LI[0, 1].

A: Given integral operator is: ∫01s3+s2xtdt ; A : C0,1→L10,1