Question: Find the eigenvalues and the normalized eigenvectors of the matrices In (b) write the normalized eigenvectors as the columns of the matrix U and show

Find the eigenvalues and the normalized eigenvectors of the matrices

(a) 4 1 2 1 -1 -2 2 24

5-20 6 6 (b) -2 -2 2 2 =C 02 7

In (b) write the normalized eigenvectors as the columns of the matrix U and show that U^TCU is a diagonal matrix with the eigenvalues in the diagonal.

Step by Step Solution

★★★★★

3.44 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The characteristic polynomial is computed from b For this part ... View full answer

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 Modern Engineering Mathematics Questions!

Find the eigenvalues and eigenvectors of the matrix (a) Use the eigenvalues to compute the determinant of A. (b) Is A positive definite? Why or why not? (c) Find an orthonormal eigenvector basis of...

Find the eigenvalues and eigenvectors for the matrix Ann whose elements are given by aij = if i = j, aij=1 if |ij| = 1, where is a constant aij = 0 otherwise

Think of the elements of a good marketing objective, which should achieve management consensus, guide subsequent decisions, and provide standards. Inquiry: Give a recent example of a good and a bad...

Practice Problems: 1. Transform (using the coordinate system provided below) the following functions accordingly: Z Y X a. from cartesian to spherical polar coordinates 3x + y - 4z = 12 b. from...

Eigenvalue/Eigenvector Part IV: Suppose A is an n x n matrix. a. What does it mean to say that a vector x E Rn is an eigenvector of A? b. Suppose A E R is an eigenvalue of A. What is the eigenspace...

An n Ã n circulant matrix has the form in which the entries of each succeeding row are obtained by moving all the previous row's entries one slot to the right, the last entry moving to the...

This problem deals with the matrix solution of the linear-variation method when the basis functions are nonorthogonal. (a) If {(i} in ( = (ni=1 ci(i is not an orthonormal set, we take linear...

Eigenvalues and Eigenvectors in Matlab 1. (20 points) Find the eigenvalues and eigenvectors for each of the following matrices: a. 1 0 1 A 10x 10 matrix with zeroes everywhere except that all...

Problem 1: Single spin in a dc magnetic field. The Hamiltonian for a spin-1/2 electron in a magnetic field, B, is given by 1 H = - B = 39H30 B, where the magnetic moment, = - 29M30, is written in...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

According to the graph below, what can be recommended (Effort stands for Sales Reps)? a. Add a sales rep to Dallas and St Louis b. Add a sales rep to Cleveland and Atlanta c. Drop off a sales rep...

A linearly polarized plane wave of amplitude E0 and wave number k is incident on a circular opening of radius in an otherwise perfectly conducting flat screen. The incident wave vector makes an...

How would the below information be completed on a From 4 7 9 7 ? The assets Phillip sold on March 2 0 are as follows: Date Acquired Asset Sales Price Original Cost Accumulated Depreciation as of...

Global Business Research the banking activities in a geographic region. What types of banking institutions and financial services are commonly used in countries in that area?

You wish to maximize the emf of an electrochemical cell. To do so, should the concentrations of the products in the overall reaction be high or low relative to those of the reactants? Explain your...

If you double all the coefficients in the overall chemical reaction in an electrochemical cell, the equilibrium constant changes. Does the emf change? Explain your answer.

Why can batteries only be recharged a limited number of times?

a common stock currently pays no dividends nd it is not expected to pay any dividends for the next 5 years. at the end of year six, the stock is expected to pay a dividend of $2.20/share. that...

Which of the following is true of internal control? - OA. Internal controls are only necessary for large businesses. OB. A company's outside auditor is responsible for the company's internal control...

COVID 19 Co. has forecast purchases on account to be $318,000 in March, $371,000 in April, $421,000 in May, and $496,000o in June. Sixty percent of purchases are paid for in the month of purchase,...