Calculate an A = LU factorization, where L is a lower triangular matrix that has all 1s in the diagonals and U is an upper triangular matrix with all 1s in the diagonals. [1 2 3 4 2 A = 3 8 11 8 14 20 4 11 20 30

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A: We use the following theorem: If A and B are two square matrices of order n, then trace of…

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A: Hi, thank you for the question. Since you have posted a question with multiple parts, as per our…

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Q: |Find the LU factorization of 4 31 -12 8 7 -4 A That is, write A = LU where L is a lower triangular…

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A: Given matrix is  123101144find LU factorization of a given matrix

Q: Calculate an A = LU factorization, where L is a lower triangular matrix that has all 1s in the…

A: Given that, A=1234258113814204112030 We need to find the LU factorization of the matrix A, where L…

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Q: Explain why each of the following matrices A is unitarily diagonalizable, without unitarily…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). 4 - 4 2 - 8 2 - 1 A = 10 8…

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Q: (5) Prove that if A is an invertible matrix, then (A5)-¹ = (A−¹)5.

A: I am attaching image so that you understand each and every step.

Q: 3) Let A = 2 -1 Find a matrix P that orthogonally diagonalizes A. Use P to com- 0 -1 pute A5.

A: Given, A=11012-10-11first we have to find a matrix Pfor eigen values of…

Q: Determine the dimensions of Nul A and Col A for the matrices. A = 10

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Q: 1. Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you…

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A: Given Result: A be a diagonalizable n×n matrix and P be an invertible n×n matrix such that B=P-1AP…

Q: (b) triangular with l's on its diagonal, and U is upper triangular. Use the results in (a) to obtain…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). -4 0 4 A= 8 3-5 8 12 13 ..…

A: Topic :- matrix algebra

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Q: Let A be the following matrix 6 5 3 4 5 9 3 1 4 After diagonalization, Pand Dare found such that A =…

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Q: Calculate an A = LU factorization, where L is a lower triangular matrix that has all 1s in the…

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Q: Which of the following is the LU-factorization of the matrix 1 0 a) Бая 0 1 0 -1] 1 1 0 b) :] 01 0 1…

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Q: (a) Compute the QR factorization for the matrix A = 1

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Q: Let A be the following matrix 8 8 3 4 5 8 4 2 3 After diagonalization, Pand Dare found such that A =…

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Q: 3 5 -3 1 12. 0 2 3 1 5 2 1 5 8 T 16. Find a QR factorization of the matrix in Exercise 12.

A: Concept: According to the Gram-Schmidt process,uk→=vk→-∑j=1k=1projuj→vk→ where…

Q: Find the LU factorization of 3 A = -9 13 3 -5 That is, write A = LU where L is a lower triangular…

A: The following steps are used to obtain the LU factorization of the given matrix A. Apply the…

Q: Find the LU factorization of -1 -3 -3 -5 13 -20 27 A = -4 10 -22 25 3 5 4 -6 That is, write A = LU…

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Q: a) Prove that the matrix A = is diagonalizable if –4bc (a– d)². What happens when –4bc = (a– d)² ?

A: Given,         A= abcd