Prove that the randomized Hadamard transformations are orthogonal transformations. Assume that the number of rows are in the powers of two.

Q: 4-2. (a). What is the coefficient of x in (1-x)9 (b).What is the coefficient of x' in (1–x)-9

A: (a)  We need to find coefficient of x7 in 1 - x9. We know that , binomial theorem ,  a + bn = ∑i=0n…

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A: As per the question we are given a multivariate optimising function.  And we have to find the…

Q: H.W: Which of the sequences {a,} converge and which diverge: 2. an 1+- 1. a, = 2+(0.1)"

A: 1. Given sequence is  an = 2 + (0.1)n Here limn→∞an = limn→∞2+(0.1)n = 2 + 0 = 2 Which is unique and…

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Q: In Problems 7-12, solve the matrix games using a geometric linear programming approach. 2 -3] 2] 2…

A: Given that for the (10) problem the matrix is given as 4-6-23 converting above matrix into a…

Q: 9. Show that the function f:x V-1 is a ring homomorphism f: Z[x] C. 10. What is the kernel of f?…

A: Given: The function, f:x↦-1, which is a ring homomorphism f:ℤx→ℂ.   To determine: The kernel of f…

Q: (b) Determine the following Laplace transforms: (i) L{cos² 3t}. (ii) L {cos ¿t sin t}. (iii) L {e'…

A: Laplace transform of following functions, (i)  L { cos23t } (ii)  Lcos12tsin12t (iii)  L { et cosht…

Q: (b) If f is a bounded linear functional on a Hilbert space H, show that there is a unique y e H such…

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Q: Clăššify quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic…

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Q: (b) Obtain the general solution of y^ prime prime +2y^ prime +y=e^ -x ln x on (0, ∞)

A: To find- Obtain the general solution of y'' + 2y' + y = e-xlnx on 0, ∞.

Q: 2. Solve the differential equation (3x? – x³ + 3y – 3.xy – y°)dx + 3(x + y²)dy = 0, - by determining…

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Q: Suppose that µ is the measure defined in item 3. What is µ(O) where O is the set of natural odd…

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Q: (b) What are the singular points, if any, of each of the following ordinary differential equations?…

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Q: Use Gram Shmidt Algorithm to build an orthonormal basis beginning from the given basis in R: (1, 1,…

A: First part: We have to find the orthonormal basis of the basis 1,1,1,-2,2,1,1,2,2 using the Gram…

Q: Let 3 -10 -6 and y = -4 -12 -11 9. Use the Gram-Schmidt process to determine an orthonormal basis…

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Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

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Q: Find the matrix of the quadratic form. Assume x is in R?. a. 3x - 8x,x2 + 2x3 b. 5x, + 18x,x2

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Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

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Q: Chain rule and implicit differentiation Suppose that F(x,y,z) = 0 defines z as a function of a and y…

A: Given that A function Fx,y,z=0 and z as a function of x, y and F is differentiable. differentiate F…

Q: to show that the given statement is true for all natural numbers n. 2. 1 + 5 + 9 + + (4n – 3) = n(2n…

A: (2) Let P(n) be the given statement i.e.,  P(n): 1 + 5 + 9 + … + (4n – 3) = n(2n – 1), for all…

Q: (2). Consider the double integral 1= ||. 72+ y? dA where R is the region of the XY plane, ven in the…

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Q: f(2) that maps: Find an analytic function w = 41. The infinite strip 0 0.

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Q: 1. Solve the differential equation (x² + y)dx + (x + y²)dy = 0.

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: Consider the solid Q bounded by the surface of equation y = x2 + z2 and the planes y = 4, z/3 = x, z…

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Q: I. Give one other possible application that are not stated in the material of the following…

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Q: 3 >(5 + v4i) i=0

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Q: A harmonic wave is traveling aiong a rope. It is observed that the oscillator that generates the…

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Q: Find the radius of convergence. Can you identify the sum as a familiar function in some of the…

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Q: Using the table

A: Introduction: Chinese Numbering System The Chinese numeration system uses characters to represent…

Q: U sing induction ,prove that : can+1)! for n>o (1) (3)(5)... (an+1) = a" n!

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Q: y dx — (х + бу?) dy %3D 0

A: Exact differential equation: The equation P (x,y) dx + Q (x,y) dy = 0 is an exact differential…

Q: Consider a system of differential equations X Ax, where x = and the 2x2 matrix A has eigenpairs d1 =…

A: To find the given options

Q: METHOD OF UNDETERMINED COEFFICIENTS Case IV : f(x) is a linear combination involving Case I, Case II…

A: Introduction: The method of undetermined coefficients is a tool to solve a higher order linear non…

Q: 4 (2). Consider the surface S of equation z = An equation for the tangent line to S at the p(2.1.2).…

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Q: 0 27. [37] (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = = -1, where f(t) · 9t Express the answer…

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Q: Problem 9: Let (V, (-,–)) be a n-dimensional real inner product space. For any ve V, denote by ov…

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Q: Let C1 be the circle r = 3 cos 0 and C2 the cardioid r=1+ cos 0. (a) Find all point(s) of…

A: We will find point of intersection by equating both r .  If f is continuous and non negative on the…

Q: Find the centroid of the region bounded by y? 8x and y? 16(x-4).

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Q: 3. Determine the general solution of the differential equation y/" + 2y" + 2y" + 2y' + y = e¬t + t.

A: Solution of differential equation is solved below

Q: Sketch the path using the following parametric equations x(t) = 3t – 7 and y(t) = 4 sin t+1 0st55,…

A: Here we need to find different points for different values of t

Q: Use (8), to evaluate the given inverse transform. (Write your answer as a function of t.) (t) dt =…

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Q: Questio. y'=6+Sy +yy=

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Q: Find the eigenvalues A1 < A2 < A3 and associated unit eigenvectors ū1, ú2, ūz of the symmetric…

A: Given matrix is A = 4-2-2-2-24-24-2

Q: Let f : A → B be a function. Prove that f is surjective if and only if, for every pair of functions…

A: Please comment if you need any clarification. IF you find my answer useful put thumbs up. Thank you.

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

Q: Example:- Find the general solution of 2) (x2 + 3y2)dx – 2xydy = 0 3) y' = e(2x+y-1) – 2 dx y+x

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Q: (a) Use the definition of L{:} to determine L {te-"} (b) Determine the following Laplace transforms:…

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