QUESTION 5 Find the LU factorization for the matrix A below, where L is unit lower triangular and U is upper triangular. What is the (3,1)-entry of matrix L? (only this value is required as the answer) A = 2 1 22 -2 6 3 -11

Q: If A is an 7 x 12 matrix, then what is rank A² + dim nul (A²) equal to? Your

A: We can solve this as follows:

Q: 11. 1 2 3 2 6 3 0 6 -6 -1 -2 -9 -1 0 7 0

A: Given: A matrix .To find: An LU factorization of the given matrix.

Q: Find the LU factorization of A = -4 5-5 8-614 That is, write A = LU where L is a lower triang with…

A: Introduction: Finding the inverse of a matrix and determining the determinant of a matrix are two…

Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below and…

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Q: Consider the matrices A and B presented below. Find the following matrix products: AB= BA= A² = B² =…

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Q: Find a matrix A that has an LU factorization where L is 4 x 4 and U is 4 x 3. L = U = 9. " 9-

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Q: Find an LU-factorization of the matrix. (Your L matrix must be unit diagonal.) [33] 56 0 LU = 188=

A: The given matrix is A=-71560. The LU-decomposition of a matrix A is factorization of matrix such…

Q: 2. Given the following matrices below, confirm or deny that (BT AT)-¹ = (A-¹B-¹)". 40*X B = 2 2 3 -6…

A: Given, A and B are two matrices We need to prove (BTAT)-1 = (A-1B-1)T

Q: Find an LU factorization of the matrix A. 3 5) A = 6 24 7 3 6 -5 22

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Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Let A be a matrix given by 3-6 -1 4 -8 -2 -3 6 3 Find a 3x3 matrix B such that B 0 and AB = 0. A =

A: A=3-6-14-8-2-363 Finding the eigen value of the matrix A A-λI=3-λ-6-14-8-λ-2-36-λ3-λ…

Q: Find the LU factorization of 4 4 -1 4 A = -12 -10 -9 12 16 -7 14 That is, write A LU where Lis a…

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Q: Let A = 0 1 0 10 Find an invertible matrix S such that S-¹AS is a diagonal matrix. What is this…

A: We will first find out the eigenvalues and corresponding eigenvectors of the matrix A.

Q: (6 :) b12 such that A and B commute, that is, A.B = B·A. (b21 (b11 10. For the matrix A = find a…

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Q: 2. Perform the indicated operations with the given matrices. Be sure to show and explain all work.…

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Q: Find the LDU factorization of -3 -6 A -15 -29 33 -15 22 That is, write A = LDU where L is a lower…

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Q: 8.) Find the LU-factorization of the following matrix 1 2 2 2 3. 1.

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Q: 1 Perform the row operation R₁R₁ on the matrix below. - -4 6-8 - 4 5 3 4 6 2 [::::)-1888 -4 5 3…

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