11. Is the following decomposition in BCNF (hint: think lossless join) R=(ABCDE)|R1(AB) | R2(BC)| R3(DE)| R4(ABD) F = {A → BC, C → DE, B→ C)

Q: 19. Prove that if {A₁, A2,. Ak} is a linearly independent subset of Mnxn (F), then {(A, A₂,..., At}…

A: 19. Prove that if  is a linearly independent subset of , then  is also linearly independent.

Q: Let c be a real number.  Define the one-parameter family f_b(x) = (x - b)(2x -3b) + x + c a.…

A: The one-parameter familyfb(x)=(x−b)(2x−3b)+x+c

Q: Suppose T: P3-M2,2 is an isomorphism whose action is defined by 3a-3c -b-3c T(ax³ + bx²+cx+d)= -3c+d…

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Q: 2. Let (X,(x) and (Y, (,)) be Hilbert spaces. For (x1,y1), (2, y2) = X x Y, put ((x1,y1), (2, 2))xxy…

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Q: Compute for (1+u+ u²)(1+u).

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Q: 3. Let z = (21, 22), w = (w₁, W₂) E C². Show that (z, w) = z₁w₁ + Z₂W₂ is an inner product on C²

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Q: Evaluate e fry²dæ + x³dy, where C' is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2)

A: We apply the green's theorem to solve the given problem.

Q: Expand а) 1 f(2) = (z – 2)(z+ 1) about z = 2.

A: We have fz=1z-2z+1 Now, using partial fraction decomposition we get for constants A and B:…

Q: Construct a idempotent of order 3, L3. Find L4 latin square of order 4, L4, and a commutative latin…

A: Given:An idempotent Latin square of order A commutative Latin square of order .Objective:Find the…

Q: Extend the proof of the Schmidt decomposition to the case where two parties A and B may have state…

A: Suppose that A and B are two parties having state spaces of different dimensionally. The statement…

Q: 2) What rule maps ABC onto A'B'C'? A. (x,y) → (x+4, y = 4) B. (x,y) → (x-3, y + 5) 4 (2-0)-²00) AY 5…

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Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

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Q: df Catx) is expandad

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Q: Q2/(A): Let L.N are submodules of M and n:M - M/N be the natural R-homomophism. Is n(L) submodule of…

A: Given that,                 L and N are submodules of M .  Also, π : M → MN is a natural R-…

Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U1v₁ + U₂V2; (b) (u,…

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Q: 6. Let T: R³ → R² be given by 74-7 8-6.5.) = T Show that I is a linear transformation by confirming…

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Q: 4.a) Show that (1+2i) is a zero of the polynomial Qcx) = x²-6x*+3x -20. Hence , or otheruwise, write…

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Q: 23. Determine whether each of these functions is a bijection from R to R. a) f(x) = 2x + 1 b) f(x) =…

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Q: Calculate the cross product between a(3;-3; 1) and b(4; 9; 2). BIU SI E : E

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Q: in(Zg++s)indeyclic grauf2enerated by I, Z,3

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Q: For what values of a does the homomorphism system (b – 1)x + 2y = 0 2x + (b – 1)y = 0 Have a…

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Q: 15. Let x = (x1, x2). Using the feature mapping show that *(2,3)·¤((4,4) –-(2,3)·(4,4)*

A: Given that for x=x1,x2, the feature mapping is…

Q: Prove that there is an (v, k, X)-design with b blocks and each element appearing in r blocks if and…

A: The problem at hand deals with the concept of designs and aims to establish a relationship between…

Q: 71. Show that the number of planted plane trees on 2n vertices, 2m+1 of which have even number of…

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Q: 5. Find LU Factorizatioon of A = [5 2 1 1 3 2 7 1 2 3 2 1- Show the work!

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Q: Use membership table to prove (AunionB) – C = (A – C) union (B - C).

A: We need to prove the following statement using membership table. A∪B-C=A-C∪B-C

Q: 16) fueluete Sx Jx+3dx 4) 리/5(x+3)기2 -2(x+3)12+c 6) /5(x+3}51z . "/s (X+3)"z + C XJX+3 dx S/2 312 6)…

A: The given integral is ∫xx+3dx.

Q: 2.5) Find the set of all sclutions in x of the following inhomogon cous linear systems Ax=b where A…

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Q: Let C ~ Cauchy(0,1). Show that C² + C-2 =9 4C² + 2.

A: c^2+1/c^2 >2 thats why it is equal to 4c^2+2

Q: Let →a=⟨−4,1,−2⟩a→=⟨-4,1,-2⟩ and →b=⟨−2,−3,4⟩b→=⟨-2,-3,4⟩. Find the projection of →bb→ onto →aa→.…

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Q: 25. Find Uge B and Be B for each collection B. BE 4 (a) + *+{[11] N}*(0) + {[L1 =): N} N}₁ B+ :n (c)…

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Q: 7. Let V={(x,y) x,y € R}. Suppose addition and scalar multiplication are defined using the following…

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Q: 4. Let A := {1,2, 3, 4} := B. (a) What is the cartesian product of A and B. (b) Find S := {(a, b)|f…

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Q: the book is "First Course on Fuzzy Theory and Applications"

A: To calculate the fuzzy definite integral with the given data

Q: Show that each of the following are not inner products on R³,

A: (a)We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and…

Q: + Crun) 2. You are given that T: U → X is a linear transformation. Prove that, T(c,u, + C2U2 + ..+…

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Q: 2. A robot performs the following operations on a set of points (x,y) in the 2D plane to check the…

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