For each quadratic function a) State the matrix of the quadratic form associated with the given equation. b) Determine the eigenvalues of the matrix. c) Construct an orthogonal matrix P with |P| = 1 that diagonalizes your matrix from a). d) Write the equation of the function in the new coordinate system. e) Identify the type of conic or quadric surface described by the equation. f) Calculate the angle of rotation in degrees. Let p = 5. Let q = 8. 1. 7x² + 4y² +7z² + 8xz − 15 = 0

Q: If three vectors vị, v2, V3 E R° are linearly dependent, then one of them must be a scalar multiple…

A: GIVEN THREE VECTORS v1, v2, v3 belongs to R^3 are linearly dependent

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A: For part (a): According to the given information, it is required to calculate

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A: We have to find out

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Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

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Q: Write the 3D Rotation Matrix around the y-axis by 0 = 45°:

A: Introduction: One kind of transformation matrix is the rotation matrix. This matrix serves as a tool…

Q: 2. Let A (1,-1,0) and B = (2,1,-2). (a) Solve for projgA. (b) Find the angle between projgA and A.

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Q: Are the vectors Choose DO-A- -5 5 2 and -10 linearly independent? 14 f they are linearly dependent,…

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Q: 2. Write the matrix that could be used to rotate a vector 200 degrees clockwise about the origin.…

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Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

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Q: 6) Find a matrix that stretches a vector horizontally (changes it's width) by a factor of 3, shears…

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A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

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Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

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Q: (d) Using matrices, find the images of the points (3,-2) and (5,1) under a rotation of 25° about the…

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Q: 6. Find Ar for A = and z= Az =

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Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: Describe the solutions of the first system of equations below in parametric vector form. Provide a…

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Q: O Find a vector perpendicular to both i- 3j+2k and 5i-j-4k

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