6 7 /hat is [AB, the coordinates of A with respect to the standard [2 4 [o _0 1 1 asis B = of R2x2? 0 0 Ex: 5 < >

Q: %3D 2. Prove that -24y of 3. =2x

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Q: 2. Use the inclusion-exclusion principle to find the number of solutions to the equation r+y+: = 19,…

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Q: 5. Prove that So*(y – 0)dydr =

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Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian. b. Establish…

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Q: Let tn be the n-th triangular number, starting with t1 = 1, t2 = 3, t3 = 6, %3D %3D etc. (a) Prove…

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Q: 6) The Ying of integers(2) is ideal of veal number (R) an DTrue D Fulse

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Q: 2 1-X ie 2=tny then prove that da

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Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: Prove that v = In (x- 2)^2+(y-N)^2 is harmonic in every region does not include the point (2,N) and…

A: Given v=lnx-22+y-N2 where N=44. So, v=lnx-22+y-442                                    ........1 To…

Q: Q.4// prove that: cothx = In, |x +1 -1 х —1

A: let y=coth-1(x) x=cothy We know that cothy=x=ey+e-yey-e-y xey-xe-y=ey+e-y Multiply ey on both sides…

Q: 6. Find a²z дгу of z = In(xy)

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Q: Q1. Verify Euler's theorem for the homogeneous funetion, fxy.2)-axy +byz + czu

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Q: In rank - sign test, the null hypothesis u = µo can be rejectedin favor of %3D the alternative u < u…

A: Signed rank test HypothesisHo:μ=μ¯oHo:μ&lt;μ¯oWe reject the null hypothesis if W+≤Wαwe reject  the…

Q: Find the infimum and supremum of the set X = {3 – Vztn ine N}. -

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Q: Use Fermat's Theorem in your proof that Vn E Z>², 2 is irrational. I

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Q: Prove that 1/(nx) → 0 pointwise, but not uniformly on (0,1) as n → co.

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Q: 2.9 Give the joint (bivariate) cdf of X and Y, Fy(x, y), in tabular form. (Copy and complete this…

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Q: 9. Prove (1, sin z, cos z} is linearly independent in [0, 2x].

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Q: i) Find an upper bound for the modulus 3z³ + 5z + 1, if |z|<1 where z is the complex number.

A: Now for the mod function: : a+b≤a+b. SO using the same method in the given complex function:…

Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: 15. Let z = 2cos0 + i(1 – 2sin0) where -n < 0 < n Show that Iz – il = 2

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Q: BIWC DAS 7.37. U₁, U₂ are independently and uniformly generated between 0 and 1 by a machine. Let X…

A: Given that:

Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

Q: What does Peano's Theorem 6.1 guarantee for the IVP dy = y cos(t2), y(to) = Yo dt O only one…

A: At least one solution exists for every (t0, y0).

Q: 6. Consider the ODE system below f = y? - ,2 = y +?. Which of the following is true? a. Solvable by…

A: Here we have given two differential equations. For a system of ODEs, we can use the elimination…

Q: 2 1 Find a mat rix P such that P- 2 0 0 3 0 3 [11 O AP = 1 0 -1 0] BP = 1 1 1 1 OCP = 0 1 1 -1 ODP =…

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Q: Soluti 03 16. A 11 22 1 Let Ax- b be a linear svstem of n eauations in n unknowns, and assume that A

A: Given: A = 03-2114225, b = 75-2  and Ax = b To find: The value of matrix x.

Q: SSR is defined by SSR = E9 - 9). Prove %3D (1) SSR = 3} S.z- (2) E(SSR) = o + Bị Sr. (3) Show MSR ~…

A: Given, SSR=∑i=1ny^i-y¯2. The fitted equation of yi=β0+β1xi+εi is  y^i=β^0+β^1xi, for i=1,2,...,n. yi…

Q: 3- Let µr1 = 2 in region 1, defined by 2x+3y-4z > 1, while µ2 = 5 in region 2 where %3D 2x+3y-4z <…

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Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

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

Q: If a (b,v,r,k,lambda) design is symmetric with lambda=1, then there exists an integer n such that…

A: Using projection property in BIBD.  We know that, Symmetric 2-designs with λ = 1 and order n &gt; 1.…

Q: 6) let fl2) = CosCitaiy) 22atey Express flz) that f satisfies in the form and fornd z So the Canchy-…

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Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

Q: Prove that v = In [(x-2)^2 + (y - N)^2] is harmonic in every region does not include .the point ( 2,…

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Q: 2. Prove 1+5+9+13+ .…+ (4n – 3) = n(2n – 1) using PMI. ... %3D

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Q: 8. Let B = and A = Verify that AB, the pseudoinverse of AB, is not equal to BA. Thus the formula…

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Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: Find Taylor's expansion of 1 about the point z =- i. i) f(z) = (z + 1)2 2z3 +1 i) f(z) = about the…

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Q: 2 (x) 2. prove that s

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Q: Consider the ARMA (2, 1. ). Ke -« Xez = process We-BWer1 %3D Find the conditions that Xe is Cousal…

A: Given information: The parameters of the ARMA process are 2 and 1.

Q: (3) Let A be m x n (not need to be square). What is the sum of the diagonal elements of ATA in terms…

A: (3) Given that Abe m×n matrix (not need to be square matrix). We have determine the sum of the…

Q: Determine Z- Trans furm in cludig vegiva of con vergence in n 7o メ(At n<o

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Q: Factor 11 + 3i in Z[i] into indecomposable Gaussian integers. Hint: use the norm to guess factors.

A: Using the norm to guess the factors.

Q: Poblam cu (a) Compute Cm 2月-/ where xe [-,]. (1) 2n 2n-1 where ze C-1,1]. (b) Gompule Cm z nっ%

A: (a)

Q: 4: a) Let X.X., X -N (Hi,6f). Let Y,, Y2 Ym-N (u2,63). .... d (1-a) % CIfor oi when ai. a known.

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Q: Nine Starbucks are located in a 3 mile by 3 mile square area in which there is a 1 mile by 1 mile…

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Q: 3. Prove that the sandwitch theorem.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.