Question 3 4 pts [Before you attempt this problem, make sure you know about matrix and...
Question 2 3 pts [Before you attempt this problem, make sure you know about matrix and vector norms and their properties in Section 7.1] Let A3x4 be a given matrix and let V4x1 be a vector. Suppose we know that || A|| = 0.82, and ||0|| = [b], then we can conclude that ||Av|| <
Question 1 3 pts [Before you attempt this problem, make sure you know about matrix and vector norms and their properties in Section 7.1] It is given that one row of a 3x4 matrix A has entries 3 70.74 -0.12. Then, we know that the infinity norm || A||- <
Question 4 3 pts [Before you attempt this problem, make sure you have learned about eigenvalues, eigenvectors, and the spectral radius in Section 7.2] Suppose we are given that a 3x3 Matrix A has eigenvalues 0.5, 2.10+16, and 2.10-16 Then the spectral radius of A equals
3. [Total: 8 pts) The purpose of this problem is to remind you of basic vector manipulation, and to get you familiar with the notation used in this class. Suppose a point charge q > 0 is at rest and located at position r = (2,3), in a two- dimensional Cartesian coordinate system (x,y). Suppose we want information about the electric field E at position r= (6,4). a) 2 pts) We will define the 'script-r' vector 1 =r-r'. Make a...
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(33 pts) This question is about the matrix = ſi 2 [3 2 0 4 1 6 3 1] 4 9 co (a) Find a lower triangular L and an upper triangular U so that A = LU. (b) Find the reduced row echelon form R = rref(A). How many independent columns in A? (c) If the vector b is the sum of the four columns of A, write down the complete solution to Ax = b
SOLVE ANY
(2.b) Pts 15 Suppose A' is any matrix whe row reduced echelon form A Show there is a matris D' Mn a wuch thnt A iDMa such that A I Question 3: The matrix condition B2B Ps 30: In this problen B is n (3.a) Pts 10: If a is an eigenvector for B, what is the attached eigenvalue (3. b) Pts 10: Irge R", why is BU) perpendieular to Bur square, n x n, smmetric matris satisfying...
Iry to hhel ieal 4 Suppose that the 3 x 2 matrix A has rank 2 and we want to solve Ax b. a) (10 pts) If there exists a solution x ()l show that 0 0 b) (5 pts) Is the 3 x 3 augmented matrix (Alb) invertible? Why or why not? c) (10 pts) Suppose that you found the solution below 2 (A | b) 30 0 Can you compute the solution to Ax = b? If yes...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
Here is the matrix mentioned in the problem:
7) Change (23 pts) Diagonalization of a matrix. For the matrix from the last problem. a) (6 pts) Find the eigenvalues of A b) (6 pts) Find the eigenvectors of A, Choose x1=1 for the first element of both eigenvectors. c) (4 pts) Is this system stable? What type of damping does it have? d) (2 pts) Find the diagonal matrix D corresponding to A. e) (1 pts) Find D3, use actual...