2. Let A be an nxn matrix over R. Consider the LU-decomposition A = LU, where L is a unit lower triangular matrix and U is an upper triangular matrix. The LDU-decomposition is defined as A = LDU, where L is unit lower triangular, D is diagonal and U is unit upper triangular. Let 2 4 -2 A = 4 9 -3 -2 -3 7 Find the LDU-decomposition via the LU-decomposition.

Q: Find an LU decomposition (factorization) of 9. 8 A = 5 3 That is, write A = LU where L is a lower…

A:

Q: | 1 2 -1 4 | | 3 3 5 0 | | 2 1 1 3 | | 4 2 2 1 |

A:

Q: Find the spectral decomposition of the matrix 可

A:

Q: Consider a linear transformation T from R to R2 for which T and T Find the matrix A of T. A =

A: We want to find matrix of given linear transformation

Q: Find the matrix A of the rotation about the z-axis through an angle of pi/2, counterclockwise as…

A: To get the matrix A for a rotation about the z-axis through an angle of pi/2 counterclockwise, we…

Q: Consider the tri-diagonal matrix Find its QR decomposition. 42 A = 2 2 0 1 1

A:

Q: Consider the bases of R2 B1={(1,0),(1,3)} B2={(0,1),(1,1)} E={(1,0),(0,1)} Correspond M(Id)_B1_E (a…

A: To find a base change matrix from B1 to E, we need to find the linear combination of basis vector in…

Q: Exercise 5: We consider the following matrices: 0 2 - - ( ) - ( ) - 0 - (9) B = 0 For the matrices…

A: A=020000AAT=020000000200        =400000000 The eigen value of the matrix AAT is 4,0,0 The eigen…

Q: Count the exact number of floating point operations (i.e., scalar addition, subtrac- tion,…

A: We will using gauss elimination method Please see the solution step

Q: Compute the singular value decomposition (SVD) of 1 2 0 A = 2 1 0 \o 0 . showing all your working…

A:

Q: 2x₁ + 4x₂x3 = 15 7x₁3x₂ + 3x3 = -4 4x13x28x3 = 19

A: Given: 2x1+4x2-x3=157x1-3x2+3x3=-44x1-3x2-8x3=19 We have to find the inverse of the coefficient…

Q: Show that LU decomposition is not possible for the matrix A, where 1 2 3 A 2 4 1 0 2

A: The given matrix is,A=123241-102

Q: Let A be a n × n matrix with Schur decomposition UTUH. Show that if the diagonal entries of T are…

A: The Schur decomposition of a square matrix A states that there exists an orthogonal matrix U and an…

Q: Find the LDU factorization of L = That is, write A = LDU where L is a lower triangular matrix with…

A: Given We need to find the LDU factorization of matrix A.

Q: For the given matrix A, the orthogonal matrix (V") in the singular value decomposition A=UDVT is:…

A: A=200021012000

Q: b) Find the QR decomposition of the matrix [2 -2 17 2 1 0 1 1 0 1 72-0

A: To find- FInd the QR decomposition of the matrix 2-21221011101

Q: Find a polar decomposition of the matrices

A:

Q: Find the LU factorization of A = 10 -15 -21 That is, write A = LU where L is a lower triangular…

A: Given: 55108-15-21

Q: Suppose that A is a 10-by-10 matrix over the complex numbers. Suppose that the singular values of A…

A: Please check the next step for details

Q: Find a matrix corresponding to the linear transformation that rotates R clockwise by 45 degrees…

A:

Q: Let 461 PART A: Find a singular value decomposition (SVD) of A. PART B: Using your answer from part…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: Show that any two rows of a matrix can be interchanged by elementary row transformations of the…

A: The two transformations are as follows:, this means that multiple row 'i' by 'k', this means that…

Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that P'AP gives the proper…

A: As this problem is related to orthogonal diagnolization of a matrix, hope you know how to find…

Q: Give an example of a real square matrix that does not have an LU decomposition. Explain carefully…

A: Please see the below picture for detailed solution.

Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

A: Here we use the gram Schmidt process to find the QR decomposition of matrix

Q: Consider the matrix A = show that the product L(X)=Ai is a linear transformation, where žER*.

A:

Q: where * denotes a nonzero number. A = LU= = dim(N(AT)) = 1 and dim(R(AT)) = 4 dim(N(AT)) = 2 and…

A: