Answer the following question 200 Let A1 = 0 0 -1 -2 Find an LU decomposition of the matrix by 1 0 1 6 following the LU algorithm namely find appropriate matrices L1 and U1 such that A1 = L,U1.

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

A:

Q: If A and B are arbitrary real m x n matrices, then the mapping (A, B) = trace(A"B) defines an inner…

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: Let QT = Gn−k · · ·G2G1, where each Gi is a Givens transformation. Let b ∈ Rn and let A be an n × n…

A:

Q: Prove that the sum of two symmetric matrices of the same size is symmetric. Prove that the scalar…

A: Solutions

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: calculate the matrix representation according to the standard bases.

A:

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: B- Find the transformation matrix of a point [1 01 2] translated by [1 5 0], rotated about x-axis by…

A: From the given information. The given matrix is . The matrix is translated by . The rotation about…

Q: Given a rate of 175 pesos per hour, how many hours should you work to earn 35,962.50 pesos

A: If ∆x is the amount earned in time ∆t, then the equation for the rate of the amount earned per unit…

Q: Suppose A is a 2 × 4 matrix, and B is a 4 × 2 matrix. Assuming that A, B act on vectors in R",…

A:

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: Use Orthogonal Similarity Transformation to transform the following matrix into Hessenberg Matrix 21…

A: To transform the following matrix into Hessenberg Matrix using orthogonal similarity transformations…

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: Let O(2, R) be the set of 2 x 2 orthogonal matrices. Describe all of the O(2, R)-conjugacy classes.

A: (1) Two elements x and y of a group G are said to be conjugates if there exists an element g in the…

Q: Consider the following 3*3 matrix A=100,1-2-2,141 Show with your calculations that the matrix is…

A:

Q: Prove why A-1=(ATA)-1AT is correct using the invertible matrix theorem

A:

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: 4 -1 5 -2 where I is the identity matrix. Let A = Compute 31 – A and (31)A,

A: To compute the following matrix

Q: Ke A transformation is defined by the 2x2 matrix Aa-a b-a Latb a where a and b are scaars. It n is…

A:

Q: Calculate matrix representation based on standard bases

A:

Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

Q: 1) Consider the "elementary matrices" 7 01 Elry - [88], Es-in-=[68], and EET-1 (8) E5-123 : 050 =…

A:

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: Construct a 4×3 matrix A and vectors ~b and ~c in R4 so that ~b is in the range ofthe linear…

A:

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: Let A be an n × n symmetric matrix of rank r. Explain why the spectral decomposition of A represents…

A:

Q: Define Hilbert matrix.

A:

Q: 2. (5pts) Find the LU factorization of the following matrix. 1 -3-5 -3 -1 -5 8 A= 4 2 -5-7 -2 -4 7 5

A: Step 1:Step 2:Step 3:Step 4:

Q: 3. (ey + 1)²e-dx + (ex + 1)³e¯*dy = 0

A:

Q: Describe all 1 by 1 and 2 by 2 Hermitian matrices and unitary matrices.

A:

Q: Calculate LU decompositions for each of these matrices (Non-anonymous questionO) 1 3 2 A = 2 8 5 2 1…

A: