10. Find U 4, and N4,, where i is a positive integer if (a) A, = {i,i+1,i + 2,.) (b) A, = {0,i} %3D %3D

Q: 9. Show that exp(iz) = exp(iz) if and only if z = nл (n = 0, ±1, 2, ...). (Compare

A: To prove that exp(iz)¯=exp(iz¯) if and only if z=nπn=0, ±1, ±2, . . ..

Q: - 21 , Prove that + (n? m' ) yn=o 2.

A: According to the Leibnitz theorem, dndxn(uv)=C0nunv0+C1nun-1v1+C2nun-2v2+... Formulae used:…

Q: Given 21 = Z3 Prove jk 13 2.

A: Given,  ∠1≅∠3 To prove  j∥k

Q: (-1)"2" /ñ Prove that if m is a positive interger, 1'(-ni +3) =1:3.5...(2m – 1)

A: I will use method of induction to prove the statment.

Q: 4 to onabans ! (0)0 4. Prove that

A:

Q: 4. Prove that for n > 0: E, 2* = 2"+1 – 1. sk3D0

A:

Q: In 26-36, write a proof. 3 12 1. a Ex. 26 Ex. 27 26. Given: mz1 + mz2% 180°, mz3 + m2 180°. Prove:…

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Q: 5. Prove that (Z, × Z6)/((2,3)) S Z12.

A:

Q: Prove that S3 = Inn(S3) = Aut(S3).

A:

Q: {2, 3} CA implies that 2 E A and 3 e A. Select one: O True False

A:

Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

A:

Q: 9. Prove L'S 25+1 Cs+2)?(S-1)2. %3D

A: Consider F(s) = 2s+1(s+2)2(s-1)2                            (1) Let 2s+1(s+2)2(s-1)2 =…

Q: Prove that S4 = ((1 2 3 4) , (1 2 4 3) ). %3D

A: As you asked for question number 8 , and hence here it is.

Q: 2. Suppose A is an m x n matrir, x ɛ Rª and Ax = b. Then b is in 1) R" | 2) R™ 3) RmfnT 4) R™n

A: Given :  A is an mxn matrix , x∈Rn and Ax=b   To find :  b is in which space of the given spaces.

Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: 3. cooficiant af z" in the apransion 3)11

A: From the Binomial Expansion

Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

A:

Q: in in Signed-Rank Test a two-sided alternative, we may reject H0 in favor of H1 if either w+ or w-,…

A: Signed rank test for  two tailedHo:M≠Mowe reject Ho, if W+≤Wα and W-≤Wα

Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: 2. Count the number of rearrangements of the word TASTE in which no letter appears in any of its…

A:

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

A:

Q: .1כ If n33, еxpand u %3D а'хх, a" x,x;

A:

Q: 5. Prove that if A and B are similar then dim(ker(A)) = dim(ker(B)).

A: We have to prove dim(ker(A)) = dim(ker(B)).

Q: 28. Compute Ak where A = [4.-3] 2 - 3.

A:

Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

A:

Q: 6. Given: 21 and 22 are complementary Prove: SX 1 WX S. 2,

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Q: 3. Show that Z, -

A:

Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

A:

Q: (7) Let S = {1- (-1)" | neN}. Determine inf S and sup S. Justify. n

A: To find inf S and sup S .

Q: 2л 2 2 Compute |pA dz dr de 0 07 O A. 35 28 O B. 35

A: To solve the integration.

Q: (2 Let xinN(0.1), n = 2 and T= Xx +X2 Show that Tis a Sufficiency Stakistic.

A:

Q: If tanh '() = 1- 12/3, then z = %3D In + 종 In O In In

A: As per the question we have to solve the complex equation and find the exact value of the complex…

Q: If In a + In(z-7) = In(4x), then z = 11 %3D

A: Since you have posted more than one question we solved the first one for you. For the remaining…

Q: Prove that (0.01)(100sin2π(5000)t)2 is equal to 0.5+0.5cos2π(10000)t

A:

Q: (7) Let S = {1- (-)" | n € N}. Determine inf S and sup S. Justify. n

A: To find the supremum and infimum of the sequence S .

Q: 15. Find the general solution of dr bcosedr + rsinode

A: General solution of differential equation

Q: Cannot solve!

A: Given complex numbers are These can be written in polar form as Now,

Q: 6. Show directly that inf(B) = 1 for B {N =: 4+1} -

A: The given expression is,  B = {1+1/n : n belong to N}

Q: 5. Demonstrate that Im(iz) = Re(z).

A: It is required to demonstrate the problem 5. Problem 5 is solved below in detail.

Q: 3) Ll a, = 5, Qz = 13, end Anta 5 anti - 6 an (n71). Prove by inbuetem that an =2* +3" (n. %3D =

A: The solution is given as

Q: 8 Show that 1+2++ In S 1|+ |r2|++|rn| for any numbers r1, 22, ....

A: To show,    x1+x2+.....+xn≤x1+x2+.....xn   for any numbers  x1, x2,....., xn . Which is generalized…

Q: 3. Suppose at a small college, 30% of the students are freshmen, and 60% of the students live on…

A: Given, The probability that the students are freshmen is pf=0.30 The probability that the students…

Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? What is the smallest…

A: It is given that p and q are prime numbers. Assume that gcdp, q=d. Then, d is the greatest common…

Q: Prove that √2+√5 is irritational

A:

Q: Solve for z: Inz + In(z – 6) = In(2z), %3D

A:

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

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

A:

Q: Show that yn Z, if n³+5 is odd then n is even

A:

Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

A: