Verify that the Galois imaginary is primitive in GF(3, x³ + 2x+1)

Q: isider the complex number 3 a = 4+i√2, where i² = -1. (a) Find the minimal polynomial of a over Q.…

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Q: Let B = {B]. A} mation x→→ Ax. =[%] be a basis for R2 and A = Find the B-matrix for the transfor-

A: Given that The transformation is

Q: a) Let a = V2+ v2 i) | Determine the minimal polynomial of a over Q. ii) | Write in terms of a…

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Q: Es A (a), B (b), C(c) and D (d) are related as x a +yb + zc + wd +z+w=0, where x, y, z and w are…

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Q: E: Let z = 1+i and z'=i-1. 2) Are these two complex numbers independant in the complex vector space…

A: We have to check for  two complex numbers independant in the complex vector space C? For this we…

Q: 25. B = (f1, f2, f3) is a basis for R2[x] where fi = 1+ x + 2x², f2 = 1 + 2x + 5x², f3 = 2 + x +…

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Q: 3-2. Prove the triple scalar product identity А (Вх С) 3 (АХ В): С.

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Q: If L and U are invertible, then (LU) – Find A from the given LU factorization: 9 -27 7-14 96 = -63…

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Q: 2) Let v be the rector space of matrices defined in R. 4 A=[ ethgiLED Find the coordmates of the…

A: Given that, A = 4-11-11-7 Let X=1-2-21, 2113, 4-1-15 Coordinate representation relative to the basis…

Q: values of (1, Ar) on the manifold where (1, B1): Let A and B be Hermitian operators on a real…

A: As per the question we are given an invariant manifold on the Hilbert space defined by : ⟨x,Bx⟩ = 1…

Q: ()-() - y +22) 2y Sei f : R → R*, (y 2x + 4z a) Geben Sie die darstellende Matrix M(f) von f bzgl.…

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Q: D: P2> P2 (Dthe differential operator so that D(ax²+bx+c) = 2ax +b); a the standard basis for P2; B…

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Q: A2 A3 Ak A1, A2,... , An all invertible,

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Q: Prove that k(x,x)=xAx' is a valid kernel, where A is a symmetric positive semidefinite matrix.

A: Let  we consider      kx,x' = xTAx'…

Q: (0+0i) 0+0i 1+0i 0+ 0i 0+0i (1+0i is the standard basis for Cn as a vector space over C and again…

A: Basis: Let V be a finite dimensional vector space over a field F. A non-empty subset B of a vector…

Q: Find the projection ofv onto u

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Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

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Q: Prove that -iEnt/th 1(0)

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Q: Find a basis for span(sin2x, cos2x, cos 2x) in F

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Q: O Let (e>+) is aring of complex numbers and Mz be aringof2 matrices aud g e-ɔM, desined as Follows:-…

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Q: 18 f1. are the corresponding Christoffel symbols and are components of two symmetric covariant…

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Q: Extend {l + x, 1 + x + x2} to a basis for P 2.

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Q: ->> Points A (a), B (b), C(c) and D (d) are related as xa + y + zc + wd = 0 and x+y+z+w=0, where x,…

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Q: 0/ Prove that the transformation w-3:+2-j is conformal.

A: w=3z+2-j⇒dwdz=3≠0

Q: True or false with full explanation The relation ‘~' on Z given by (a,b)~(c,d)⟺ (a-b)| (c-d) is an…

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Q: Let V=R₂₂ [x] with (the inner product, 1 <f(x), g(x)) = f(x) g(x) dx Find a basis for the or…

A: Answer is not correct, since the second element is not orthogonal to x2+x+1. Please check and verify…

Q: Extend {1 + x, 1 + x + x2} to a basis for P3.

A: Given set is ,                  1+x , 1+x+x2   (.)  Standard basis of  P3  is                    1 ,…

Q: Prove that a square complex matrix is unitary if and only if its columns vectors form an orthonormal…

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Q: ow that B = {5+i, 2+i} is a basis for Q(i) whose elements are algebraic tegers. Why is ß not an…

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Q: 7. Prove that M2x2(C) is a complex vector space under the usual addition and scalar multiplication…

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Q: Without using determinants, show that {(2, –x,,3x²,x³} is a basis for Ps then find dimension for P3

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Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ

Q: Let v = (−2,3,0,6). Find all scalars k such that ∥kv∥ = 5.

A: The given vector v=-2, 3, 0, 6. We have to find all scalars k such that kv=5.