Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis formed by the three kets {Je1>, Je2>, Je3>}. In the basis of these three vectors, taken in this order, the Hamiltonian H^ and the two operators B^ and D° are defined by: 3 i 0 -i 3 0 0 2 7 i 1 - 0. 2a A= hwo B= bo -i 7 1+i D= 2a 1+i 1-i 6. 2a -3a where wo and bo are constants. Also using this ordered basis, the initial state of the system is given by: (e1|v(0) (e2| v(0)) (e3| v(0)) 2 |v(0)) = 3 6 Q: What is the probability that the system will be found in the ground state after measuring H at t + 0? Q: After measuring H at t + 0, the operator B was measured. What is ± AB?

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

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A: We have to write in linear combination form

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Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Consider a physical system whose three-dimensional state space is spanned by the orthonormal basis…

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Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

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Q: (a) Show that the vectors ui = (3, 1,0), u2 = (-1,3,0) and uz = (0,0,4) form an orthogonal basis for…

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Q: What are the conditions for a set of vectors {ai , i ∈ [1, N]} to form a basis for an N dimensional…

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Q: Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the…

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Q: Recail that two nx matrices A and B are Similer if there is an invertible matrie P Such thet p' Ap…

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Q: Fnd a basis of the Subspaca of R* by five vectors spanned (1,2,1,-1) (10,15,15, 0 (3,4,5,1)…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: Determine whether the given orthogonal set of vectors is orthonormal. If it is not, normalize the…

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Q: Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an…

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Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

Q: Use Gram-Schmidt process to transform the basis {(1,1, 1), (0, 1, 1), (1, 2, 3)} into an orthonormal…

A: Given: Basis v1=1,1,1 , v2=0,1,1 , v2=1,2,3

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

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Q: find a homogeneous linear system of two equations in three unknowns whose equation in three unknowns…

A: For the solution of the problem follow the next step.

Q: b) Find an orthonormal basis spanned by a set of vectors V = (2,2,1), V2 = (-2,1,2), V3 = (9,0,0).…

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Q: A type (0,4) tensor Tabed satisfies Tabcd A® µ°A°µ¢ = 0 for all con- travariant vectors X and uº.…

A: Tensor of type (0, 4): A tensor of the form Tabcd is called covariant tensor of type (0, 4). A…

Q: Find invertible matricer A and B Cuch th at A+ B is singular. Find cingul ar matrices A and B such…

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Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

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Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Linear Algebra

A: According to the given information, it is required to construct an orthonormal basis of the set:

Q: Decide whether the vectors [2,9,-1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8, 14,…

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Q: On an 0rthonormal basis of a set of vectors, determine which is right or wrong and explain it. ty…

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Q: If u and v are orthonormal vectors, show that P = uuT + v vT is the standard matrix of an orthogonal…

A: Given: If u and v are orthonormal vectors To Show: P = uuT + v vT is the standard matrix of an…

Q: The set of vectors u = , and u2= are Linearly dependent having rank 1 having rank 3 Linearly…

A: In this question, we need to check whether the given set of vectors are linearly independent or…

Q: The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

A: Using coplanarity conditions we have

Q: Obtain a set of orthonormal vectors by Schmidt method: u = (1, 1,0,1), uz = (2,0,0, 1), uz (0, 2,3,…

A: According to gram Schmidt method  orthogonal vectors can be obtained as: x1=u1x2=u2-<u2,…

Q: orthonormal

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Q: Determine whether the given orthogo­nal set of vectors is orthonormal. If it is not, normalize the…

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Q: The set of vectors u = , and u2= are having rank 3 having rank 1 Linearly independent Linearly…

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Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 0, -2), (2, 3, 4) is

A: We will solve the problem

Q: Consider the set of vectors S = {u= (-1, 2, – 1), v= (2, – 5, 0), w= (1, – 3, – 1)}, then find the…

A: u=-1, 2, -1,  v=2, -5, 0  &  w=1, -3, -1. Now, u·v=-12+2-5+-10=-12 u·w=-11+2-3+-1-1=-6…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: Given the basisof R° consisting of the three vectors n = (-1,0,0) , ½ = (0,1,0) and V3 = (0,-1,1) .…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: let have innos psoduct. Lu,V) = UiVit 2U2V2+ Suzue where u= Lui,uz, Us) and V=LUI, Vz, Vz). Use…

A: Given, ℝ3 have inner product u,v=u1v1+2u2v2+5u3v3, where u=u1,u2,u3  and  v=v1,v2,v3. Need to…

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A: To find subset of vectors that forms a basis for the space spanned by the vectors. Form a matrix:…

Q: 9. Determine if the vectors å = [-1, 2, 1], b = [-2,4, 2], and ở = [12,8, 1] are coplanar. %3D

A: given vectors a=[-1,2,1] b=[-2,4,2] c=[12,8,1]

Q: Find an orthonormal basis spanned by a set of vectors V1 = (2, 2, 1), V2 = (−2, 1, 2), V3 = (9, 0,…

A: We will first find orthogonal basis using Gram-Schmidt Process, then orthonormal basis

Q: Compute the standard basis of Nul(A) for the matrix (No need to show work for calculating rref)

A: Find the Null(A)

Q: If the scalar (dot product) of two unit vectors is zero, they are a) Linearly dependent b) Forming…

A: For the given statement we have to choose the correct option.