ii) Given Z, = -1 + iv3 and Z, = -v3 + i, show that In (Z,.Z2) # InZ, + InZ2

Q: b) Show that z, + z, = z, + Z, . 2

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

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

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Q: Suppose two members of the group of twelve insist on working as a pair---any team must contain…

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Q: 17. Find a, b, c in Q such that (1+ V4)\(2 – V2) = a + bV2 +cV4 Note that such a, b, c exist, since…

A:

Q: Consider the following. u 3 (-4, =(-4, 6), v = (1, 1) (a) Calculate projy u.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 9. Express the gcd(117,213) as a linear combination of s and t such that gcd(117,213) = 117s + 213t…

A: To write the gcd(117, 213) as a linear combination.

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: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: 3. Show that B = {0, 1, 2, 6, 9} is a difference set in Zjj. What are the parameters of the SBIBD…

A: For the given question ,t he first thing to do is to find the value of λ. Then, we will proceed…

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

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Q: If ZH and LJ are supplementary in HJKL, are a) ZK and ZL necessarily supplementary also? b) ZH and…

A: Given :∠H and ∠J are supplementary…

Q: 1/3 If (x+iy) =a+ ib, Prove that

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Q: Compute In(z) dr.

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Q: 6. If u=,%) prove that xu, + yu, + zu, = 0

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Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

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

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Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

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Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: If A = 2x²,-3yz, xz² and qp = 2z - x³y. Evaluate A Vop and A x Vp at the point (1, -1, 1).

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Q: Prove or disprove Arg)- Arg(z,) - Arg(z,)

A: The polar form of the complex number, z=x+iy , can be written as z=rcosθ+isinθ , where, r=x2+y2 and…

Q: If z,,z,€C then Zz=Z2 OZi+Z2=Z,+z2 OZi+z2=0 Z,Z2=0=Z,=0 or zz=0

A: 2nd and 4th options are correct.

Q: 3. Show that Z, -

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Q: 4. Demonstrate that Re(iz) = -Im(z);

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Q: 4. Prove that, VR, -11-

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Q: 12)List the first five berms of Ehe regence a,=6, aan= 5a -4 as=3 a=? asz?

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Q: U is a neighborhood of x0 and U ⊂ V, The V is a neighborhood of x0. (2) If U1 ...., U2 are…

A: Solution ::

Q: Evaluate S"2 in (cscr) Szye-2dzdydx

A: Suppose a multi variable function f(x,y,z) . To evaluate the integral notice the below result :

Q: В 3 0. -2 12 15 10 -7 2 -3 0 15 0. 12 0 10 anglusis (on ugur own pgper), and determine the

A: This is a problem of linear transformation, linear algebra, matrix algebra.

Q: Cannot solve!

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

Q: Prove S^2 is simply connected.

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Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

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Q: Prove: 4 x,,x2x, ER, then |x, +x, +.. + x,| s |x,|+|x,|+... + |x,|

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Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: 5. Prove by taking z = a + bi, z – z = 2iIm z.

A: 5) The given complex number is z=a+bi. Here, Rez=a and Imz=b. For any complex number a + bi the…

Q: True or False   Consider the following model, Yi = β0 + β1Xi + ui,E[ui|Xi] = 0,i = 1,...,n…

A: Solution: As per the guidelines first three parts should be answered.

Q: Let u= (4,15) and v=(2,-3,1). Then (2u+v).(u-3v) is equal to:

A: Given,    u=4, 1, 5, and v=2, -3, 1

Q: List the sides of AFGH in order from least to greates if mZF=(5x+6)°, mZG=(12x-4)°, and m…

A: Consider the following △FGH: m∠F=5x+6°m∠G=12x-4°m∠H=4x+31° Sum of all angles of triangle is 180°.…

Q: c) Compute µr, Hy, Ož, o, Cov(X, Y), and p

A: Reviewing information, Given pdf is, f(x,y)=x+y                 ; 0≤x≤1 ,  0≤y≤1

Q: Prove that azdə † czbz and dib dzbz

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Q: Given: mZB = 42° and mZACD = 78° %3D Prove: mza = 36° %3D a 42 78°

A:

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: Prove that √2+√5 is irritational

A:

Q: . Prove that, e²i = e²1=22. ez2

A: Let,z1=x1+iy1z2=x2+iy2z1-z2=x1+iy1-x2+iy2=x1+iy1-x2-iy2z1-z2=x1-x2+iy1-y2…

Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||

Q: 8. Following the idea of Exercise 6 and referring to Exercise 7, express the positive gcd of 49,349…

A: