Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

Q: Write the 3D Rotation Matrix that first rotates around the y-axis by 0, = 45° followed by a rotation…

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Q: Check the screenshot for the matrix question:

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Q: b₁ b2 = = Multiply the following matrix / vector pair to obtain the vector b. 1 [ 3 ] [5] - [၁] =

A: Matrix multiplication

Q: Find an LU factorization of the following matrices а. 1 4 -1 7 -2 1 -4 6 –1 -2 -3 1 -1 7 Determine…

A: From the given information. The matrix A is as follows.

Q: Find the (1, 2) cofactor of the matrix A = b) 2 d) -18 f) -9 e) 18 9 3 4 -1 2 -1 2 3 -3 -3

A: given A=32-1423-1-3-3 cofactor of Element (1,2)=-11+2M12=-M12 where Mij=minor of (1,2)

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

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Q: [5+7i] 3+4i b) A (2+9i) [5+7i 3+4i

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Q: b₁ b₂ = Multiply the following matrix / vector pair to obtain the vector b. 2 (30-0 = 1

A: Given that the matrix equation 123412=b1b2

Q: [2 Given that; a=1, b=2, c=0, d=1 Explain why the matrix a b c d is not diagonalisable.

A: Here the given matrix Let x be tha eigen value of A matrix Then

Q: For the matrix A = 0  1 −6  5 1  0  2 −1 3  1  0   2 Determine if the vector v = (−7 5 8) is in…

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Q: 2 Consider the matrix A = and the vector u = Let B = (A – A)² and define vector v = Bu. If v = write…

A: We use the properties of matrices to answer the given question.

Q: entries

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Q: Let u and v be column vectors from Rn and define A = I + uvT, where I E Rnxn is the identity matrix.…

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