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: Let ū = (-1,2,4) and ū = (-3,5, 2). Compute the following: (a) ū+ū (b) .공 (c) ||해 (d) ũ - 7 (this is…

A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

Q: give the general formula of this amount b.) choose those polynomials that contain elements of the

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Q: u = 3i – 2 j+4k v=i-3j-k 18) (Section 9.7) Find the cross product in space i j KI 3 -2 4 -3 -1|

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Q: (Q. +,.) is a subfield of (F = {a + bV5: a, b e Q}, +,.); (F = {a + bv5: a, b e Q}, +,.) is a…

A: A non-empty subset F' of a field F is a subfield of F if F' is closed with respect to the…

Q: Use the inner product = aobo+ aıb1+ azbz+ asb; to find , lIlp|], d(p, q), and then find the angle…

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Q: use Gauss Fordanmetrecd to Solbe the fellowsing setafeg Qe linear 2X+ -4x2 +6X3=5 A +3X2-783=; + 5…

A: Introduction: A system of linear equations can be solved using Gauss-Jordan elimination method. This…

Q: 7. 2) Write the difference equation for the systems shown below. ii) Find yon) / xen). yon) x(n) 3…

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Q: 2) Let R real numbers, define = x,Y1 +4x2y2 + 6x3Y3 for x = (x1,x2, X3) and y (y1,y2, Ya). Is inner…

A: Let V be a vector space over ℝ.An inner product <·,·> is a function V×V→ℝ with the following…

Q: Show that is isomorphic to Z2.

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Q: The set of polynomials {1, x² + 3x“, 2x² – 7x4} is a linearly independent set in P4.

A: NOTE: Due to time limit answer of 1 is given here, for other please ask in a different question.…

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: xʻy Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (x4+6y8) r4.

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Q: Investigate the stability of the following sys (Consider the quadratic form as lyapunor system.)…

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Q: Let V3 = {(a, b)|a, b E R} with the following operations: (a₁, a₂) + (b₁,b₂) = (a₁ + b₁, a₂ + b₂)…

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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: 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: Find gcd (272, 1479) and find the integers x, y such that gcd(272, 1479) = 272x + 1479y

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Q: Use the inner product (o, 9) = 2obo +a1b1 +a2b2 to find o, 9), |P||- |||, and d(p, a) for the…

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Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: We have to show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

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

Q: 5. Show that the function that sends an ordered pair ((x1, x2, x3), (Y1, Y2, Y3)) of elements in R³…

A: I have write answers below Explanation:

Q: Use the inner product =p(-2)q(-2) + p(0)q(0) +p(3)q(3) in P3 to find the orthogonal projection of…

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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: 2. Using the Singular Value Decomposition, show that for any square matris A, it follows that A* A…

A: Given Data: We have to show that for any square matrix A, it follows that A*A is similar to AA*.

Q: Letflx): 3x-2:9 x)=5x+1 Compute the indicated Values, a, lfogl (3) blfef) (oJ d, (gog) (-7) )e.…

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Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: Please compute x and y such that 117x + 17y = gcd(117,17), 52x + 56y = gcd(52,56), and 123x + 126y =…

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Q: Construct two bijections from (0,1) to (1,1/0).

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Q: Find a basis for the eigenspace of the eigenvalue λ = 3 for the matrix A = 4 2 3 -1 1 -3 2 4 9

A: We will find the basis for the eigenspace of the given eigenvalue.

Q: Find a number z (except 0) such that Az³ + Bz²+ Cz = D 2 1 3 0 -2 -4 00 ^-[ ] ³-R2 :]-[+]-[1] B= 1 2…

A: Solution

Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: Compute: gcd(51, 42) Find a pair of integers x and y such that 51x + 42y = gcd(51, 42) (x, y) = (…

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