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Q: If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a…

A: If A is diagonalizable and B is diagonalizable then it is not necessary for AB to be diagonalizable.…

Q: Parameterize (in 2 variables u, v) the paraboloid 4x2 +y2 -z=0

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Q: If C is the center and A, B are two points on the conic 4x² +9y² - 8x - 36y + 4 = 0 1 1 13 such that…

A: The  equation  of the conic is given by  4 𝖝2 +  9 𝔶2 - 8𝖝 -36𝔶 +4 =0⇒(4𝖝2 - 8𝖝+ 4 ) + ( 9 𝔶2…

Q: Prove that the dual of (P1) has a finite optimal valı

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Q: 9. Explain in your own words how to decide what kind of conic it is if you have the equation Ax? +…

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Q: Given the matrices: i) ii) 01 1 0 2 2 3 A 3 ^-(29) 8 - (-) -- »-( ) 01 B 0 = (²₂) D = 1 5 0 1 4 3…

A: a) Given that, A=010301-201B=210-143C=32D=23-15

Q: Use the properties of diagonalization of matrices to identify the given conic section:…

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Q: 3 4 Let A be 4 -3 la. Set up the characteristic equation and own value for A

A: :GivenAs per our guideliness we are supposed to solve only one part. Please resubmit other part…

Q: 1. Suppose that there are 4 particles on the x-axis with masses 4, 1, 5, and 7 with coordinates 3,…

A: We know that the mathematical expression for the centre of mass can be given as…

Q: The vertices of the hyperbola y = 5+ ( x² + 9 )0.5 are Select one: O(0,-3) and (0,3) O(8,0) and (…

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Q: Let Q be the cube with vertices {(1, 1, 1), (1, 1, −1), (1, −1, 1), (1, −1, −1), (−1, 1, 1), (−1,…

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Q: 1a. Set up the characteristic equation and own value for A 1b. Set up a diagonalmatrix D and an…

A: Given that A be                        344-3

Q: 20) Find the coordinàtes of the foci of the conic x² –10x –16y² – 64y – 55= 0

A: We write the given conic in standard form Then we compare it with the standard equation of a…

Q: a b - Let B be a real matrix similar to a matrix A of the form -b a B = Q'AQ. How would you sketch…

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Q: 1. Find the equation of the conic whose only vertex has coordinates (-1/2,1) and passes through the…

A: Since the conic has only one vertex it is a parabola. This idea will be used to solve the problem.…

Q: 3. Find a rotation matrix to transform the quadratic equation to standard form, then use it to find…

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Q: 2. Is it possible to determine a vector i so that vet is a solution to the system 2 X'(t) = (; )…

A: According to question, Given system, X '⇀t = 1243 X ⇀t

Q: what is the dimension of the vector space formed by the solution of the system of the following…

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Q: b) Prove: Let A be an m x n matrix, R" = NS(A) + RS(A). %3D

A: A be an m×n matrix, we have to prove that ℝn=NSA⊕RSA  …1.

Q: 5. Write the equation of the following conic 12 11 10 4 3 2 -1 3 5 fo 11 12 -1 -2

A: The given conic is the ellipse with  1. Center (8,5)  2. Vertex1: (8,12) 3. Vertex2: (8,-2) 4.…

Q: Stable molecules form when atoms arrange in a way to exert equal force on each other. One such…

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Q: a) Given the following matrices a = -and c= nd 2. 3 and C = 2. i) AT C. i) 2(BC"). i) D if (2AB)" =…

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Q: Divide the quaternion on the right 5 + 4i− 6j  of the quaternion 3i+j-2k

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Q: Determine whether the Diophantine equation 15x + 53y = 17 is solvable or not. If it is solvable,…

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Q: Write the system in vector matrix form: 21 4 e 21 3e 21 -e -4 e* 21 21 b) О x' 3e -4 e" X, 1 x 3e 4…

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Q: 16. Which equation represents the given parabola?

A: We want to find the equation of given parabola.

Q: Show that the ellipse x*/a? + y*/b? = 1 and the hyperbola x/A? – y/B² = 1 are orthogonal…

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Q: Explain why the hypercube Qn, n > 2, is hamiltonian.

A: This is a problem of graph theory.

Q: of the transformation r = u? + v?, y = 2uv is 9. () The Jacobian 4u? + 4v². a(u,r)

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Q: Calculate the equation of the system of conic sections with basic points A(1,2); B(2,0); C(-1,1);…

A: As per the question, we are asked to find the equation of the system of conic sections that passes…