0. Show that C[-1,1] c C[0,1]. C[0,1]).

Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

Q: 69. Let F(x, y) = (x,0). Prove that if C is any path from (a, b) to (c, d), then F. dr (o2

A: Given: F(x, y) = <x, 0>. C is any path from (a, b) to (c, d).

Q: Prove that if h E L'(R) and [ h= 0 for all s E R, then h = 0.

A: Use the Leibniz integral rule: For ∫axbx fx, tdt Where -∞<ax, bx<∞ We have, ddx∫axbx fx,…

Q: let H = {n² |n E z*}, determine whether it is closed under

A: Given : H={n2|n∈Z+}   To Check:  H is closed under binary addition or not

Q: Let E={(r,0,z) : os es T, OS zs 1, 5Vzs rs 5. Compute

A: Introduction: The triple integral ∫∫∫Ef(x,y,z)dV with the region E=(x,y,z):a≤x≤b, c≤y≤d, e≤z≤f can…

Q: 4. Assuming that the c possible subset of R (c) f(x) = V5 –

A: Use the definition of domain and range to solve this problem

Q: . Finish showing the Complementary Slackness Theorem by establishing that under the hypothesis of…

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Q: let H = {n² |n e Z*}, determine whether it is closed under

A: Here, we have H=n2| n∈ℤ+. To show the set is closed under binary multiplication. This means we have…

Q: Prove that r(z) = (In-)²-'dt , Re(z) > 0.

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Q: Prove that S4 is not isomorphic to D12.

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Q: 3- prove that w = w yx if w = xy² + xy +

A: Given problem:- w=xy2 +x2y3+x3y4  Prove that wxy =wyx

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

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Q: verify that (A + B)T = AT + BT

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Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

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Q: Prove that c = cn. i=1

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Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…

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Q: 1. Let f(x,y, z) = vx + /y- Vz +In(49 – x² – y² – z²). Evaluate f(4, 4, 4).

A: Substitute the values

Q: Prove that if a e R, then a 0 = 0 = 0 · a. Suppose x, y, z E R. Show that xz = yz if and only if…

A: We will prove the given statements.

Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

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Q: Prove that T2 is chaotic on 1.

A: Given that T2=2x0<x<122(1-x)12<x<1 The maximum for T is 1 at x=0.5. The dynamics of T2…

Q: Prove that ifx > 3 and y> 4, then xy > 11.

A:

Q: if u=f(x,y), x=g(w) and y=h(w), using chain rule, what is ∂u/∂w?

A: Silution : Given that u = f(x,y)

Q: Determine the value of c so that the pmf of X is valid. 2 cx :-1, 1 P(X) = { c (x + 1), x = 0,2

A: Answer - Given PMF of X                 P(X)  = cx2x= -1, 1c(x +1)x = 0, 2 Find the value of c

Q: © If g(x, y) = In then xgx - vgw in simplified form is [c].

A: The objective is to solve partial derivative problem and explain process.

Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: b) Prove that if x <y and z<w, then x+z<y+w.

A: Given: Suppose x&lt;y and z≤w. To prove: x+z&lt;y+w.

Q: Suppose T: R + P, has an action on a

A: Given, And

Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: Q1:- Let T =- where W-N(0, 1) and V~xShow that T2-F(1,r).

A: We know that  The ratio of chi-square divided by its degrees of freedom is called the…

Q: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

Q: Example 3.8. Forx = 1,2,3 and y = 1, 2, let the joint pmf of X and Y be defined by I+y fx,y(r, y) =…

A: XY X=1 X=2 X=3 Total Y=1 2/21 3/21 4/21 9/21 Y=2 3/21 4/21 5/21 12/21 Total 5/21 7/21 9/21 1

Q: Let E = XE[0, + 0) } then Sup E Маx E- %3D %3D x+ O True False

A: In this problem we have to determine Sup E and Max E, and check Sup E =Max E is true or false.

Q: Let x, y, z E Z be such that both odd, and z is even. Prov

A: Introduction: Even and odd numbers are distinguished by the following characteristics: Even Number:…

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: 2. Use Wronskian to show that fi = x, f2 - Inz, and fa C (R). z Inz are linearly independent in

A: First we will calculate the wronskian of given functions f_1,f_2,f_3

Q: Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x,g (y) = 3y + 4 and h (z) =…

A: Given, Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x, g (y) = 3y + 4 and…

Q: show that if Z ~ N(0, 1) and Y ~x²(n) with Z and Y to be independent, then T: n

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Q: T: M22 ---&gt;M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---&gt; M2×2. We have to find the…

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

A:

Q: 1. Let 1, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

Q: Show that |Re(z)|+|Im(z)| < v2|z| for any z e C.

A: The solution is given as

Q: 2. Let X ~ U[0, 1] and Yn = X. Prove that Y, 4x.

A: Given that, X~U0,1 Yn=n-1nX

Q: 2) Suppose S,T E L(V) are such that ST = TS. Prove that null S is invariant under T.

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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: Find conditions on a, b, c, and d such that

A: Find conditions on a, b, c, and d such that  B=abcd commutes with both 1000 and 0001 For any matrix…

Q: 2. Use Wronskian to show that fi = x, f2 = ln x, and f3 C (R). x In x are linearly independent in

A: ANSWER:

Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

A: