Question: We consider the matrix A such that: A = 4 2 2 2 4 2 2 2 4 1. Check that the matrix A is

We consider the matrix A such that: A = 4 2 2 2 4 2 2 2 4  1. Check that the matrix A is orthodiagonalizable then factorize A. 2. Give the spectral decomposition of A. 3. Either u = (x1, y1, z1)^t and v = (x2, y2, z2)^t  R^3 . Show that the application (u,Av)= u^t Av defini a scalar product of R^3

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

2 -1 3 1. Consider the matrix A = -4 2 k 4 -2 6 a) If A is the coefficient matrix of a homogeneous system of linear equations, determine the number of equations and the number of variables. b) If A...

Algorithm 6.7.1 of the class notes is as follows: 1. We consider the matrix 4 2 -6 4 2 2 -3 1 6 -3 13 0 4 1 0 30 E R4x4 (a) Calculate the matrix factor R of the Cholesky decomposition A RTR by using...

Use NumPy notebook to check your answers Please i need help with d, e. f, g, h. 1. Consider the matrix 3 -1 A un - 1 2 8 4 0 7 9 Answer the following questions: (a) What is the dimension of the...

Linear Algebra Questions 7. Consider the matrix A = [4 8 0 2 4 0 0 0 10] Check that the vectors bl = (2,1,0), 112 = (1,2,0), and D3 = (0,0,1) are eigenvectors of A by computing the products A131,...

MATLAB Directions In order to guarantee that management fully understands the process, you have mapped out the following steps to ensure you have captured the process and have data to support your...

(MATLAB ONLY)(MATLAB ONLY)(MATLAB ONLY)(MATLAB ONLY) Directions In order to guarantee that management fully understands the process, you have mapped out the following steps to ensure you have...

Need help with this MATLAB. Could you please explain as well and just simple code. Thank you PROBLEM 3: Let An be the n x n matrix with 8 on the main diagonal and 3 elsewhere. For example, [8 3 31 A3...

Only final answer no need for explaination Section 1.5 Elementary Matrices: Problem 12 (1 point) Consider the following Gauss-Jordan reduction: -6 54 -9 1 0 0 1 EA EEA EEEA EEEE,A Find 1 0 0 E= 0 0 0...

Consider the matrix 2 5 ] A: 4 4 1 I: I5 2 (a) Determine for which value of k the determinant of A is zero. (b) When it takes this value, use row operations to find all possible solutions for x to...

8. Consider the matrix A = (a) Verify that A = 2 is the only eigenvalue of matrix A. (b) Determine a basis for the eigenspace of the matrix A corresponding to the eigenvalue A = 2. Is A...

Refer to Exercise 4.23. In exercise a. Are the events A and C independent? Justify your answer. b. Are the events A and D independent? Justify your answer. c. Compute 1 P(A | B) and P(|B). Are they...

1. Find a parametrization of the entire surface obtained by revolving: (a) C: y = cosh x around the x axis (catenoid). (b) C: (x - 2) + y 1 around the y axis (torus). (c) C: z = x around the z axis...

Topic: AHP An investor wants to buy stock for retirement and is considering 3 companies: Costar, Moderna, and Costco. He has identified 4 factors to consider and wants to use AHP to select the...

Chris borrowed $200,000 to be repaid in 120 equal monthly installments, beginning one month from today. The interest rate on the loan is 5.5% APR, compounded monthly. How much principal on the loan...