Find the coordinate matrix of x in R^ relative to the basis B'. B' = {(5, 0), (0, 2)}, x = (10, 8) [x]g = B'

Q: Show that the matrix is skew – Hermitian and hence find the eigen Values and eigen vectors

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Q: , find the orthogonal projection matrix on the subspace defined by the equation: 2х-у-3z-0.

A: a) Let v1 = [3,6,0] and v2 = [0,3,-1] be two vectors on the plane As we have 2(3)-6+3(0) = 6-6+0 =0…

Q: Define Ts Ma,2 Mara by -> Find Hhe eigen vectors valves and of T basis of selative M2,2 to eigen…

A: First find the characteristic equation.

Q: Find the inverge of the 2x2 matrix Cos t Sin t - Sine Cose

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Q: Based on this matrix calculate the false positive rate.

A: Here use given matrix and formula of false positive rate

Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: Find a singular value decomposition of the 2 by 3 matrix with entries: 3, 0, 0 0, -1, 0

A: The given matrix is A=3000-10 The matrix can be calculated as ATA=900010000  It has eigen values…

Q: Find the matrix corosponding to rotation of 90 degrees about x-axis and then find it's Eigenvectors…

A: Eigenvalue: A real/complex number λ is called an eigenvalue of the matrix A if for a non-zero vector…

Q: 7. Find a 2 x 2 matrix that reflects vectors in the (x, y) plane across the x axis. 8. Find a 2× 2…

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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: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

A: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

Q: Verify that the matrix is orthogonal.

A: We have to verify that the given matrix is orthogonal: cos ϕ-sin ϕsin ϕcos ϕ To check the given…

Q: What does it mean that matrix A is orthonormal? What does it mean that matrix A is positive…

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Q: Express the vector (-1,5, –6) in R³as a linear combination of (2,0,7), (2,4,5) and (2, –12,13).

A: Solved below

Q: The Hamiltonian operator of a system is H = -(dI dx) + x. Show that Nx exp (-x/2) is an…

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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: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1,…

A: Introduction: The Gram–Schmidt system is a way for orthonormalizing a fixed of vectors in an…

Q: Find the vector in component form with initial poi

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Q: Linear Algebra

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

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: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: Expand the 3D pollutant transport equation in vector notation into individual differential equations…

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Q: Eigenvector must be a nonzero vector.

A: Eigenvector must be a nonzero vector.   An eigenvector of a n×n matrix A is a nonzero vector v in Rn…

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: If Pis the projection matrix onto the line through (C) (:) and then I - P projects onto the line…

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Q: Let x and column n-vectors, y be two linearly independent where nz 2. Find all where eigenvalues of…

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Q: Choose the 2 by 2 nondiagonal matrix such that its eigenvalues are different positive numbers…

A: We first write a 2×2 non diagonal matrix whose eigen values are different positive numbers then we…

Q: Find the flux of ỹ across S.

A: In this question we need to find the flux across the surface is part of sphere of radius 9.

Q: 3. find the length of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2)

A: Solution :

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

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Q: stable

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Q: 1) A =| °, find fundamental matrix eta

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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: Find the rotation matrix that could be used to rotate the vector by –20° about the origin. Take…

A: Here we have to find the rotation matrix that could be used to rotate the vector [1  1]' by -20°…

Q: Show that Foranyeigen value Tofthe nonsingu lar matrix A with any natural norm Then

A: Given, Eigenvalue λ of non singular matrix A To prove : 1∥A-1∥≤λ≤∥A∥

Q: There exits a symmetric matrix with two eigenvalues, where one eigenvalue corresponds to (1,2, – 1)…

A: For the detailed explanation follow the next step.

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 the basis of column space of the matrix A given in the attached image .Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1,…

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: Find two 2 × 2 nonsingular matrices whose sum is sin- gular.

A: From the given question,, To find the two 2 × 2 nonsingular matrices whose sum is singular.

Q: A Find the variadle of matrix Baccordiag to equntrm DEUD +4I'= B , where D=PAP cmd Pis te eigen…

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Q: What is the vector where it is orthogonal to the eigenvectors

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Q: Find the stable vector of this Matrix:  0 0 1 0 1/2 1/2 1/3 2/3 0

A: A stable vector is a probability vector such that PW=W.Let W=xyz. Then, we have 0010121213230xyz=xyz…