Which of the following statements involving sigma notation is always true? Ο Σακ- b) = Σ b-Σα ) k=1 m+n B(ak)+ (ar) = Z (ak) k=1 k= η η E (ak bx) = E (ak)- (bx) k = 1 k =1 k =1 (ax+bx) = E (ax) + 6 k=1 k=1

Q: The expression (ΣW)cycle=(ΣQ)cycle applies only to systems undergoing cycles. a. True b

A: The first law of thermodynamics states that, during an overall communication between a system and…

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

A:

Q: Prove that Σan σ(d) φ (n/d) nτ (n) and ΣIn τ(α)φ(n/d) σ(n). ||

A: As per the question we are given two sum identities including the Dirichlet convolution :…

Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

Q: Let 7'(t) = (3+ 4t, cos(t), 6e*) and F(0) = (7, 2, 5). Determine 7(t). †(t) = (, , )

A:

Q: Show that if an = 3n3-17n2 + 2n-6, then an = Θ(n3).

A:

Q: 1. We can generalize our approach to warto for any state function. Consider: f = 3x²³ - 2xy² for X₂…

A: As per the question, we will verify the above for f=3x3-2xy2. We are given that xi=1, yi=2; xf=5,…

Q: Prove that (a) P(En F) = P(E)- P(En F) (b) P(EnF) =1-P(E) – P(F) + P(En F)

A: Solution: 6. Here, it is needed to prove that

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: Let G = Z5®U(7). The identity of G is %3D (1, 1) (0, 0) O (0, 1) None of the choices O (1, 0)

A: Use the property of external direct product to find the identity of the group G.

Q: EM- IM• 4. 4. 5. Express A. С.

A: Given that: (x1-μ)2+(x2-μ)2+(x3-μ)2+(x4-μ)2

Q: Let H = {(1), (12)(34), (13)(24), (14)(23)}. Find the left cosets of H in A4 (see Table 5.1 on page…

A: Given H = (1), (12)(34), (13)(24), (14)(23) in A4 H =4and A4 =4!2 =12 So , Number of distinct left…

Q: Show that if Y = ax + b (a = 0), then Corr(X, Y) = +1 or -1. We know Cov(X, Y) = Cov x, ])--)-I + b…

A: We need to show that, If Y=aX+b then Corr(X,Y)= +1 or -1

Q: Let A = 1 2] and A = xA + yl , then the values of -5 1 x and y respectively are -1 2 (a) IT'11 규·규…

A: We will solve the following

Q: (a) Find the left cosets of {e, (1, 2)} in S3. (b) Find the right cosets of {e, (1, 2)} in S3.

A:

Q: Suppose A E C such that X(2+i, 3 – i) = (5- i, 7- 5i). Then (1) A = (1– i) (2) A = (2– i) (3) Does…

A:

Q: Find the singular values σ₁ ≥ σ2 of 01 = 02 -1 -27 A = -2 1 -2 2 9.

A: Find the singular values σ₁ ≥ σ₂ of the matrix A: Singular values of a matrix are the square roots…

Q: Show CO PLETE solutions. 1) Show that Laguerre's ODE, Table 7.1, may be put into self-adjoint form…

A:

Q: Use Parseval's identity to compute 1 n=0 (2n + 1)²

A:

Q: az Find for z = e2z-y.

A: Given : z = e2x - y

Q: Use 2.2.24 to solve 2.2.25 My argument should work for any alpha and any z_*

A: The objective of the question is to use the reasoning of Example 2.2.24 to show that the limit of…

Q: Let yII + yI - 42y = 0 Find all values of k such that y = ekx

A:

Q: 1, thên kX KX < ky

A: Here are real numbers such that if , then

Q: Example 19-36. If U, = a + bx+cx², prove that 3 U, dx = 2U2 + 12 (Uo- 2U2 + U4) 1 and hence find an…

A:

Q: Q-12)-for the model below Max z=10X1+5X2 st 4X1+2X2540 3X1+3X25 30 X12 0, X2 20 MAX Z=- O 75 O 100…

A: Linear programming. Graphical method