let (X; Z) v it piece wise comnected ?

Q: ||x||3 < ||x||1|||| VI 22

A: As it is known, L2 norm of x is given by x2=∑i=1nxi21/2 L1 norm of x is given by x1=∑i=1nxi L∞ norm…

Q: Use the sub no spaces: T-2y = - %3D 3x + 2y

A: Given that: x-2y=-10           ........(1)3x+2y=-14      ..............(2)

Q: Бxї Zet (x, г) бе space, then Co-countable тебя xis not Тз-брасе

A:

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: Let S in Mzx2; a + 2d=0 and b-2c 0 with the standard %3D operations in M2x2 Which of the following…

A:

Q: Y Show that f (2)= 2+ Con formal maps %3D on %3D

A: Given that,f(z)=z+1zz=1

Q: Assume X, Y CU. Prove that (U \ X) U (U \ Y) = U \ (X n Y)

A:

Q: What is the difference in ndahin befween matnx multiplicatin and fensor multiplicahin of two lensors…

A: The tensor product V ⊗ W of two vector Spaces V and W (over the same field) is a vector space,…

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: (а) Show that Ах (В x C) 3D (А:С)В — (А: В)С

A: As per bartleby guideline for more than one question asked  only first is to be answered please…

Q: Let A Find grad(div( A ) %3D

A:

Q: o Show that X2 = {(x, y) E X x X : x<y} is a sublattice of X x X. %3D

A: Given that X is a lattice. To show that X[2]  is a sub lattice of X×X. It is enough to show that,…

Q: Let X and Y be two T, spaces, then X×Y. :is

A:

Q: 4).ェ Pare subset, -f y such that CeD than fic) is not eD, then the Convers %3D そイue.

A: Solution As it's mention C=D and f^-1 same , so each and every element from  f inverse we get equal.…

Q: State the Squeeze Theorem carefully.

A:

Q: Let f(x) = 3x² and. P = {–2, –1, 0, 1, 2, 3}. Compute Lf(P) and U,(P). %3D %3D

A: Consider: fx=3x2 and P=-2,-1,0,1,2,3. Compute LfP and UfP.   If P is a partition such that…

Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

A:

Q: 3) By changing the independent variables x and y to u and v by means of the relations u xay, v = x +…

A: Apply chain rule

Q: let (X, Z) %3. üit piece wise comnected ?

A:

Q: Let v = Does {v1, V2, V3} span R*? Why or why not?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: X Y Z' WXXN W. Y ED O XYZ' + XY + WX'YZ (XYZ)+(X+Y) + WX'YZ F

A:

Q: Let r, y EN such that y # 0, then y+r#0.

A:

Q: Let f(x, y, z) = x²y°z – xyz², and compute: (a)

A: In this question we will use basic of vector  calculus i.e gradient of any function and curl of…

Q: Y is neither on the interior, nor the exte Y lies in the interior or in the exterior of Y lies on…

A: In this question we will use basic of algebra. We will use basic concept of interior angle and…

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: uppose A is a diagonali= . Would this be true if

A: Given, A is a diagonalizable n x n matrix whose eigenvalues are all 1 or -1.

Q: prove V injective if x1 ‡xn → v(x1) = v(xn)

A:

Q: f (て) be a top. space 3.ト X-Tab, cidiel (xて) be top space %3D %3D et A= {bj. FindO A Tb,d] %3D 2.…

A:

Q: Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.

A:

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

A:

Q: Consider P2 with the inner product = f (x)g(x) dr. Then d(x, 2) Jo

A: d(x,2) represents distance between the vectors x and 2 P2 is the set of all polynomials with degree…

Q: Let f(x, y, z) = xyt + z3 and x = st², y = s³t² , and

A: The given function is fx,y,z=xy4+z3 and the values of x, y, and z are st2, s3t2, and s2t2…

Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: Let w = f(u), where u = x g(y), show that w,xx = f" (x g(y)). g²(y). %3D

A: Let w=f(u), where  u=x g(y). So using the chain rule, differentiating with respect to x, we get…

Q: Show That R is Banach Sface.

A: To Show -

Q: -x+y<y. 2 If x < y, prove that x <

A:

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

Q: Let z = 2 - 3xy?+ x². Zay %3D Zyy

A:

Q: Prove using soundness (Required): (∀x)A → (∀x)B ⊬ (∀x)(A → B).

A: The proof is shown below.

Q: Find the norm of the image of U(7, 8) by an reflection about y-axis

A: To Determine :-  The norm of the image of U 7 , 8 by an reflection about y- axis.

Q: Let A = %3D

A:

Q: Show that X is Hausdorff if and only the diagonal A = {(x,x) | x € X} is closed in X x X.

A:

Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…

Q: Find, ∂f/∂u (deltaf/deltau) and  ∂f/∂v (deltaf/deltav) in terms of u and v if, f(x,y)=y/x and and…

A: Find, ∂f/∂u (deltaf/deltau) and  ∂f/∂v (deltaf/deltav) in terms of u and v if, f(x,y)=y/x and and x=…

Q: Qz\ show that ?_C=0} is not a swbopace of R

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.