1 0 2 -1 0 2 0 1

Q: Find a matrix A such that 5 ¹0-08-08-0 A 5 A A = A =

A: We can solve this as follows:

Q: Diagonalize matrix A, i.e., find diagonal D and invertible P such that A = PDP-1, where -[:] 3 2 A =…

A:

Q: Find an LU factorization of the following matrices а. 1 4 -1 7 -2 1 -4 6 –1 -2 -3 1 -1 7 Determine…

A: From the given information. The matrix A is as follows.

Q: Consider an m × n matrix A and an n × p matrix B. Show that the row vectors of AB are in the row…

A: Let A be m×n matrix and B is n×p matrix. To show that the row vectors of AB are in the row space of…

Q: Given the vector x = (1, 2, 2)T , find a Householder matrix that will zero out the last two entries…

A: Given: Vector, x=1, 2,2TTo find: Householder matrix H

Q: Let x and y be distinct vectors in Rn (i.e., x = y), and let A be an n × n matrix with the property…

A:

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

A:

Q: Let A be a symmetric positive definite n×n matrix and let S be a nonsingular n × n matrix. Show that…

A: To show that STAS is positive definite, we need to prove two things: 1. STAS is symmetric. 2. For…

Q: 3 Orthogonally diagonalize the matrix A = giving an orthogonal matrix P 4 and a diagonal matrix D…

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

Q: Le+ A=22 1 Find on orthogonal matrix Q and a 2-1 diagonal matrix D such that A=QDQT.

A:

Q: Determine the Householder matrix that annihilates all but the first entry of the vector v = [2 22…

A: Let α=2222T Then take, v=α-αc1=2222-α2000=2222-α000 ,Here α=±||a||2=±2 Now , since,α1  is positive ,…

Q: Let A be an n × n matrix and {v1, v2,..., vk } a linearly dependent set of vectors in Rn. Are Av1,…

A: Linear dependent: A finite non empty set of vectors v1, v2, ...vkis said to be linear dependent if…

Q: If A is a triangular matrix, when is R = rref(A) equal to I?

A: We write the row reduced echelon form of a matrix A as rrefA. A square matrix is said to be an…

Q: Show that if A is an m × n matrix such that AAT is non- singular, then rank A = m.

A: Let AAT can be non singular only if the columns in A are linear independent and they span the column…

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

A: Given matrix  A=2300320000230032