Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

Q: EX/ show that im Cosy-1

A: Given limit is : limy→0cosy-1y To prove  limy→0cosy-1y=0 Use the trigonometry formula,…

Q: A population consists of 4 units with values 156, 149, 164 and 155 respectively. Draw all possible…

A: Given that Population size N = 4 Sample size n = 2 Then possible samples WOR are NCn = 4C2 = 6

Q: Show that [x, p;] = iħ.

A: note :  As per our company guidelines we are supposed to answer ?️only one question. Kindly repost…

Q: How many invertible functions exist with the signature Za→ Zb if a = b? %3D

A: To find the number of invertible functions from ℤa to ℤb. Given that a=b. Also ℤa has a elements.…

Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: Show that im n /-

A: Limit of the sequence

Q: In Z3×U3, Find the order of (1, 2). Show your work.

A:

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

A:

Q: gion enclosed by y

A:

Q: sen } 4

A: Let us find the Z transform of the given sequence in the next steps.

Q: Find In zdz. Preview will appear here. Enter math expression here

A:

Q: Prove H'n(x) = 2nHn−1(x), n = 0, 1, . . .

A:

Q: Find integers x and y such that 3220x + 6006y = gcd(3220,6006).

A:

Q: 4) State the Rank-Nullity Theorem.

A: To state: Rank - Nullity theorem.

Q: The number of reducible monic polynomials of degree 2 over Zz is

A: The number of reducible monic polynomials of degree 2 over Z3 is

Q: find rank(AT) and nullity(A)

A: Rank of A = rank of A^T use this relation

Q: : Does fcz) = Continuous af cis

A: We have to solve given problem:

Q: Which term of the expansion of (z + 4) contains z Term number contains z4.

A: Given expression is: (x4+4)16

Q: Compute In(z) dr.

A:

Q: Verify that there is no magic square of order 2.

A: We will verify that there is no magic square of order 2 using the proof by contradiction.

Q: Theorem: Proper ies of Transposes 3.) %3D

A: If we take transpose of transpose matrix, the matrix obtained is equal to the original matrix.…

Q: Show the the Sar induce

A: According to the given information, it is required to show that equivalent norm on a vector space X…

Q: Use linearization to approximate In(1.2).

A: we can use the following formula for approximate calculations: f(x)≈L(x)=f(a)+f′(a)(x−a). where the…

Q: Verify Eular,s theorem for z =ax2+2hxy+by2

A:

Q: Show that (an) is increasing

A:

Q: Prove that • I %3D

A:

Q: Show that Z4 is not isomorphic to U(12) by comparing the orders of elements.

A: z4=0,1,2,3 is group w.r to +order of elementsoa=n⇒an=e where n is least positive…

Q: What is the Increasing,Decreasing, and Constant Therom

A: Definition of increasing, decreasing and constant theorem

Q: Find the deriratire of y tanx usim the Difinition Rule

A: Given that:y=tanxTo find its derivative.

Q: Express E: livenr coumbination of Ÿ; = and V as a

A:

Q: Show that A° = A°-0- and A-o = A- %3D

A:

Q: prove that esch'x - In (* + x2 %3D

A:

Q: Let S = {2x, 1 –- x, x2 + x- 1, x + 1}. Then S is a %3D

A: for a basis we need to check that a set must be linearly independent and spans the whole vector…

Q: Find the value of MZACD.

A: Given,            The figure of a square ABCD is shown below :

Q: Let H = Span{1+x,1+x², 3+x +2x², 2 + x + x²}. what is dimH?

A: Solution

Q: Verify Eular's Theorem for z=ax²+2hxy+by2

A: According to Euler theorem,  x∂z∂x+y∂z∂y=nz Where n is the degree of the homogeneous equation.

Q: Can the sum of divisors of zero be an invertible element?

A: The objective is to state whether the sum of divisors of zero be an invertible element?

Q: I, Let dlP) S-a). End fIt) Sta

A:

Q: Show the Complete S lu fwn i 3 ナ *

A:

Q: be run under the building. If these two blocks must always be next to each other, how many s can the…

A: Given Here we have 7 blocks ,but we  have to keep 2 perticular blocks together. So we have to…

Q: Let X1,..., Xn be Show that Y = min(X1,. %3D Show that

A: From the given information, X1, X2,.....,Xn are independent, Xi~expλi The density function for Xi…

Q: ion Prove that for

A:

Q: Express x8-x as a product of irreducibles over Z2

A: We have to express x8-x as a product of irreducible over Z2. Definition:- Irreducibility is defined…

Q: A complwx number z is a number of the form z=x+iy, x,yER

A: Both the statements are TRUE

Q: what expressi on is equivaient to this. (n-a)!

A: n!(n-2)!+n=n×(n-1)×(n-2)!(n-2)!+n  [we use the idea of factorial]=n(n-1)+n=n2-n+n  [distribute n]=n2

Q: Let Z, = { 0, 1, 2, 3, 4, 5, 6 } where each x e Z, is a least residue when an integer is divided by…

A: (4) Given that ℤ7=0, 1, 2, 3, 4, 5, 6, where each x∈ℤ7 is a least residue when an integer is divided…

Q: 3. Prove that the sandwitch theorem.

A:

Q: let FQ) = -2Xidefined on [14], then UC Pmif) =

A: