5 6 0 4 0 0 0 0 -1 -2 7 3 A = (2) 1 1. The matrix A can be decomposed using partial pivoting as PA= LU, where L is unit lower triangular, U is upper triangular, and P is a permutationm matrix. Find the 4 x 4 matrices U, L, and P. 2. Given the right-hand-side vector b = (26, 9, 1, –3)", find x that satisfies Ax = b.

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

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Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: Find the transpose of the Attached matrices

A: Transpose of a matrix is obtained by interchanging the rows into columns and columns into rows.

Q: [2 -1 1] A = |1 1 2,x = |y| and b = |b2 [-1 5 4] a. Determine if the columns of the matrix A span…

A: We have to determine  whether the column of matrix A can span R^3

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Find the LU factorization of A = A = 9- -4 E -4 That is, write A = LU where L is a lower triangular…

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Q: Q2. For the matrix, A = (a) Find 2 Tr (2 A). (b) If A = 21 8 7 4 6 7 5 4 find (A)-².

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Q: 3 Compute x using the vectors w = -4 and x = 2 - 5 2 x = (Simplify your answer. Type an integer or…

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Q: -1 -1 | | 4. For the semidefinite matrix A = -1 2 -1 write x' Ax as a -1 -1 sum of two squares.

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Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: 9. Do the columns of the matrix A = 7. span R

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Q: Let. A=[3,2,1;4,2,3;-2,1,-3] Convert the matrix unit using elementary operations

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Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: Determine the coefficient matrix A, the right-hand side vector b, and the augmented matrix, A of the…

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Q: Find the transpose of the resulting matrix: -100 A = 2 3 4 x 5 2 5-4

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Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

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Q: Find an LU-factorization of the matrix : 4 1 2 5 1 2. 3 - 7 6 14 16 11 1

A: Recall: LU factorization by using Gaussian Elimination method

Q: 1 6. Given that A = -1 and B = Which of these matrices equal (AB)'? -2 0 (c) 0. (a) 0. (b) (d) -2 -2…

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Q: Express the matrix A-¹ as a product of elementary matrices using In= EkEk-1...E₁A. 100 220 313 A =

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Q: 1. Consider the matrices 0 4₁-(13), 1 3)₁ 4₂2 - ( -8 -2) ₁4₁ = (3-2). 0 1 3 -5 -4 A₁-(3) -4 0 and A4…

A: We have to match the given matrix with the function represented in the graph

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: Let A, B be 4 x 4 matrices. Find two matrices so that rank(A) = rank(B) = 2 and rank(AB) = 1. A = B…

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Q: Statement: "Let A and B be n x n matrices, where the columns of A span IR" and B is not equal to the…

A: The given statement is false.

Q: 1 3 Find a QR factorization of the matrix A = 1 4 0 2

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Q: A = [2 -1 0 1; 3 5 7 -1; 1 4 2 7] List the row and column vectors of the matrix.

A: Given :                 A = 2-101; 357-1 ; 1427 To find :               List the row and column…