In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a correct expression for z;? O a Zj = (u))"x Zj = (u(®)"x Z; = (u0))"x; Od Z; = (u0)"xx

Q: 2 Evaluate: :S,vte-t² dt.

A: Detailed explanation mentioned below

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: (c) w = 5ln(7r + 8) %3D O u = r' + 8, w = 5lnu O u = 7r, w = 5 (Inu + In8) O u = In(7r), w = 5 ln(u…

A: w=5 ln(7r+8)

Q: If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e…

A:

Q: Show that For all z E C, with z # 0, then: |z/²z=1 = z

A:

Q: - Let X1, X2, ...,Xn~N(0,0) and T = Fi (T),Var(T)

A:

Q: f(x, y) = In(4 – a² – y?) + fonksiyonunun tanim kümesini belirleyip tanim kümesini koordinat…

A: for defining ln function :4-x2-y2>0x2+y2<4            .....(1)

Q: It x~N(μ,σ"), then ²~. Option 2 ption 1 *** *** *** N(0, 1) G(1⁄2,2) x² (2)

A: Given, if x~Nμ,σ2 Then x-μσ2

Q: {o, c, s}. Find two values of c in (0, 5) such that Uf (P) = 21. %3D Let f (x) = x on [0, 5], and…

A: Given : f(x) = x on [0,5] Partition of the interval P = {0 , c , 5 }. Uf(P) = 21

Q: s(2) f(z) is analytic in C

A: Ans : false

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: السؤال 27 If z,z2=0 -zz=0 or z2=0 0 صواب ihi

A:

Q: Min. z = 4x1+3x2 s.t. 5x1 + 3x2 2 15 4x1 + 2x2 < 16 X1 20,x2 2 1

A:

Q: O let X be fe VrV Finel ECX) ael E(x)

A: Note: As per guidelines we can answer only one question at a time. I request you to please repost…

Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

A:

Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: locally Lipschitz in (t,x)E[a, b]x D.

A:

Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

A:

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

A:

Q: 4 16 Define T: R? - R° by T(x) = Ax, where A = 1 3 -

A:

Q: (17) Define S(n) as follows: n S(n) : i(i!) = (n+ 1)! – 1 i=1 Prove Vn e N1, S(n).

A: Consider the given expression. Sn=∑i=1nii!=n+1!-1 Now, use the mathematical indication to prove the…

Q: 2. Let X~N(u, o2). Show that the MGF of X is etHtc²a².

A:

Q: Q/Use Definitien 13.4-1 +o prove that f(x,r}>x+y' is difterentialeat (o,0).

A: Given function is  fx,y=x2+y2

Q: o In general a;jk(Xi + Yj)Zk = a¡jkX¡Zk + AijkYiZK - True - False

A: We have to prove or disprove that

Q: The coordinates of the holes on the plate. x (in.) y (in.) 2.00 4.2 4.25 5.5 5.25 5.8 7.81 6.2 9.20…

A: From the given information,  x0=2,x1=4.25,x2=5.25 and x3=7.81yx0=4.2, yx1=5.5,yx2=5.8, and yx3=6.2…

Q: B. If f = x²cosy + y²sinx then show that fry = fyx ух

A:

Q: Calculate Ehe Value of:(o00001 (0000001A in GF () witlh vmc) =x°+x+X++

A: It is given that

Q: 4 Evaluate f, S, 6xy² dydx

A:

Q: 3. Suppose that the pmf of X is x-1 1. p(x) ,t = 1,2, 3, . 3 3 Find the mgf of X.

A:

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: Prove that du Inlul + C where n= -1 u

A:

Q: 6. Evaluate 1 x² + y² + x² dV, where E = { (®,g, z) |1< n? +g? +z? <4}.

A:

Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

Q: (7 In GL(2,Z,), det O 35

A: Option 1 is correct.

Q: What is the best substitution to make to evaluate S O u = 3x Ou = e³x u=1+e³x Ou = e-3x e³x 1+e³x dx…

A:

Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

A:

Q: c) Evaluate ſ x*(In x)²dx

A:

Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

Q: In Z, let H = &lt;5&gt; and K = &lt;7&gt;. Prove that Z = HK. Does Z = H X K?

A: Given: In Z H=5K=7

Q: 13. If w(x,y) = In(1+xy²), show that 2wxx + y³Wyx = 0. %3|

A: Given: w(x, y)=ln(1+xy2)  To show: 2wxx+y3wyx=0 Chain rule : ddx(f(g(x))=f'(g(x))g'(x) Quotient…

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.

A:

Q: Show for Re(z) > 1 -dr = r(2) ((2). %3D et - 1

A:

Q: How we dlittiluwrI x fasy)- z=0 The answer is af DE Kindly gue me alelail.

A: given function is                                                        f(x, y)-z=0 now…

Q: 4) Let x, y, z E Zg. Prove or disprove the following: Ifxy = xz, then y = z.

A: