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 1 - 2a H= hwo | -i 30 0 2 B= bo -i 7 1+i D= 2a 0. 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|&(0) |v(0)) = e3| v(0) 6. Suppose that the initial state |4(0)> was left to evolve until t + 0. Q: After measuring operator Ď and then B, what is the probability of finding the system in ground state?

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: Let u1 = (-1,1,3), u2 = (2, 1, –3), uz = (3,0, 1) are three vectors. %3D Find expansion of the…

A: We have to write in linear combination form

Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: Use the inner product (u, v) = 2u;V, + uzV2 in R2 and the Gram-Schmidt orthonormalization process to…

A: In the question it is given basis for ℝ2 is -2,1,2,1 and also given inner product by…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

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

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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: A vector is rotated about the Y-axis 45 degrees and is subsequently rotated about the fixed X-axis…

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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: Find an orthonormal basis of the plane ¤1 + 5x2 – x3 = 0. %3D

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Q: Find an orthogonal basis for A1, A2, A3 (i.e., find 3 mutually perpendicular vectors u1, u2, u3 with…

A: The solution are next step

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: The vectors (2, 2, -1) and ( -1, 2, 2) are orthogonal. Divide them by their lengths to find…

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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: Find a vector in 3d space whose magnitude is 4 and whose components have the largest possible sum

A: Find a vector in 3D space whose magnitude is 4 and whose components have the largest possible sum.…

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: Use the inner product (u, v) = 2u¡v, + uzv2 in R2 and the Gram-Schmidt orthonormalization process to…

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Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

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: 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: Find the coordinate vector of [4, -2, 1] relative to the ordered basis B= ([0, 1, 1], [2, 0, 0], [0,…

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

A: From the given matrix we can write ,x1+2x2-x3-2x5+7x6=0x3+8x6=0⇒x3=-8x6x5-8x6=0⇒x5=8x6from -x ,…

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…

A: We know that, if {v1,v2,…,vk} be a subset of k distinct vectors of ℝn,then {v1,v2,…,vk} is an…

Q: Find an orthonormal basis for the subspace spanned by (0,1,2), (-1,0,1) and (-1,1,3).

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

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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-&lt;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: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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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: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

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: 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…

Q: Find a subset of vectors v1 = (1,0,1,1), v2 = (-3,3,7,1), v3 = (-1,3,9,3) and v4 = (-5,3,5, –1) that…

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: (a) Show that the vectors u1 = (3, 1,0), u2 = (-1,3,0) and uz = basis for R3. (0,0,4) form an…

A: Answer

Q: 2(b) Th picopert matrix not to Prove matria does r

A: A matrix is defined as a rectangular array of numbers or objects. The arrangement takes place into a…

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)