Q3)B) Let X is pre_Hilbert space. Prove that (α₁x₁ + a²₂x₂, [²₁=1 P₁y₁ ) = α₁ [₁₁ B₁ (x₁₁3₁) + 11₂ [1₁1=₁ Ñ¡ (x₂.3₁)

Q: Theorem 6 If (b+ f) > (c+r) und (d+g) > (e+ s), then the necessary und sufficient condition for Eq.…

A: (P+Q)2 = P2 +Q2 + 2PQ P2 +Q2 + 2PQ = (P+Q)2 P2 +Q2  = (P+Q)2 - 2PQ

Q: -25 (1+j2 2-j5 ) = 57 + j24 2 \3+j4

A: We need to simplify the expression -2521+j23+j4-2-j5-j and show that it is equal to 57+j24 Consider,…

Q: what are domine, Vange and null space o F Tisra-s Ty Rom R?into Re 1

A: The given functions are                                 T1:ℝ2→ℝ2 such that T1ξ1,ξ2=ξ1,0.T2:ℝ2→ℝ2…

Q: Q3. Prove by using logical equivalence method: (pr) V (q+r) = (p Aq) → r

A: Two propositions are referred to as logically equivalent if their truth value is always same. When…

Q: Prove that Vn > 0: 2º + 21 + .…+ 2" = 2n+1 – 1. ... an+1_1 Prove that Vn > 0: aº + a² + .….+ a" =…

A: Here, the objective is to prove the following: 1) 20+21+22+......+2n=2n+1-1   ; n≥02)…

Q: 2 is a counterexample of vxay(x = 1/y), where the domain for all variables consists of all integers.…

A:

Q: @ (3.+j4)*

A: Since solve the first question for you. If youwant any specific question to be solved then please…

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A:

Q: 4 Lonsider the functlan fx)= -5x4- |l+x?tx-17. functfon Fex)= -5xH-|l+x²+2x-17. 5xH-113+ Whatis r n…

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Q: The product of sum (max term) form of the boolean function F = x +y'z is

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Q: Consider the set = {x € R¹ / 93x₁ +34x2 +26x3 + 18x4 ≤ 131, X₁, X2, X Show that x₁ + x2 + x3 ≤ 2 is…

A: Here, in the question a set is given : X={x∈R4/93x1+34x2+26x3+18x4≤131, x1, x2, x3, x4 ∈ {0, 1} } We…

Q: 7 (V3 +4} = - = - 64 (V3+i) 2) Using de Moiver's formula prove that:

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Q: 1 Evaluate using Convolution theorem : L

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Q: (a) A = [í 21 B = R s c= D= -2 -5. 4 = G ) B= = L, ) = 5[ -3 -5 (b) A = [; ) B =[ D = 5 -11. -5]

A: Givena)A=2112, B=-30-2-5 , C=-2-402, D=0000.b)A=1114, B=-3-50-11 ,C=19-110 , D=-55-20-25To find All…

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 10. dt 1+ 64t2 -1 A) 2sin-1 8 B) C) 2tan-1 D) 2tan-18 A B D.

A: Since you have asked multiple question,As per our policy we will solve the first question for you.…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

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A: We have to find Cauchy Principal Value of the given integral.

Q: prove that the covariant derivate satisfies leibniz's rule

A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

Q: 92+91 Let z be a point that lies on |z| = 2 and f (z) = 243 Then |f(z)| is i2-22+31 O >1 O »3 O None…

A: Given fz=9z+9iiz¯−z2+3i and z be a point that lies on z=2 We have to find the  fz Taking modulus…

Q: let fai) = -x+7| -1-342| whare XER GIue Explietly expression for z y the full Bmupliyind

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Q: Show that the embedding of part (g) takes lines to "lines."

A: (h) We have to show that lines from ℝ2 maps to lines in P2. Lines in ℝ2 will be of the form ax+by=0.…

Q: 1 0 -2 0 0 0 1 0 0 0 0 0 0 3 1 0 0 1 0 0 0 0 0 0 0 1. Assume that A~ 0 -4 1

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Q: (6. Consider the functran fa)=x² to Draw tronsfomue tim -f(x-2)-1 b for the quadratse equation…

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Q: 8. Find lcm(143, 227), lcm(306, 657), and lcm(272, 1479).

A:

Q: 3) Let f(x) = 1 + 3x on [-8, 2]. Find the number c that satisfies the mean value theorem. a) O C= b)…

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Q: B\ If X is Pre-Hilbert space then (x,ŻB,Y, ) = ΣP, (x,y, (x, j=1 j=1

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Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: + a3 + a5) – (@2 + đ4)I 4 [(a1 + a3 + as) – (a2 + a4)] [(B1 + B3 + B5) (a2 + a4) + A (B2 + Ba) (a1 +…

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Q: Let M-{1, 2}. Then O IP(MxM)=4 None of the mentioned O MxM={1, 4} O MxM={(1,1),.(2,2)} O IP(M×M)|=16

A: It is a set and relation problem

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A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: ) find w=4 +iv if the function. in term of 2 is f(z) = (Z-32²) (2z+i)

A:

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: Assume a1,a2,...,an are positive numbers, a1+a2+...+an=1. Prove: Please use non-calculus method)

A:

Q: RECURSION RELATIONS: L Jp(x}] = ° Jp=1(x), d.r Jp-1(x) + Jp+1(x) =2J,(x). Jp-1(x) – Jp+1(1) =…

A: As per our company guidelines, we are supposed to solve only the first three subparts. Kindly re…