Question: Set A = magic(4) and t = trace(A). The scalar t should be an eigenvalue of A, and the remaining eigenvalues should add up to

Set A = magic(4) and t = trace(A). The scalar t should be an eigenvalue of A, and the remaining eigenvalues should add up to zero. Why? Explain. Use MATLAB to verify that A - tl is singular. Compute the eigenvalues of A and a matrix X of eigenvectors. Determine the condition numbers of A and X. Is the eigenvalue problem well-conditioned? Explain. Perturb A by setting
A1 = A + 1.0e-04 * rand(4)
How do the eigenvalues of Al compare to those of A?

Step by Step Solution

★★★★★

3.39 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Since A is a magic square the row sums of A tI will all be 0 Thus the row ve... 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

Document Format (1 attachment)

949-M-L-A-E (947).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let A be a matrix with eigenvalues Î»1. . . . . . Î»n and let Î» be an eigenvalue of A + E. Let X be a matrix that diagonalizes A and let C = X-1EX. Prove (a) For...

Let be an eigenvalue of a linear operator T: V V. Prove that the eigenvectors of T corresponding to are the nonzero vectors in the kernel of I - T.

Let be an eigenvalue of A with associated eigenvector x. Show that + r is an eigenvalue of A + rln with associated eigenvector x. Thus, adding a scalar multiple of the identity matrix to A merely...

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...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.6 Problems Find...

explain how this application would be related to industrial engineering PART 1 (60 points) - Image compression and data analysis Figure 1: Lena. The digital images are represented with matrices. Each...

Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as...

GROUP WORK 5. Use (4) to show that equation (1) can be approximated by the difference equation With = (2 - -2) mi - Bi-1, (5) where y = wi. Explain why yo = y. = 0. 6. Let n = 5, so the rod is broken...

Show that: ap P-R

One pump can fill a gas tank in 6 hours. With a second pump working simultaneously, the tank can be filled in 4 hours. How long would it take the second pump to fill the tank operating alone?

Karl has asked you about the record keeping requirements for the business. a ) Karl is considering allowing credit to customers who purchase coffee machines from the business. Research the internet...

Define above-normal (economic) profit, normal profit, and economic loss and explain the relevance of these terms in explaining industry behavior.

a. Show that ( is a linear transformation when b = 0. b. Find a property of a linear transformation that is violated when b ( 0. c. Why is ( called a linear function? RR

An affine transformation T: has the form T(x) = Ax + b, with A an m ( n matrix and b in. Show that T is not a linear transformation when b ( 0. (Affine transformations are important in computer...

Given v ( 0 and p in, the line through p in the direction of v has the parametric equation x = p + t v. Show that a linear transformation T: maps this line onto another line or onto a single point (a...

Which of the following statements is not true? A. A purchase invoice is a source document that tells a business how much to pay a vendor. B.Revenues must always exceed expenses. C. On a correct trial...

des Compute yield-to-maturity for the following zero-coupon bonds: 1-year zero-coupon bond, traded currently at 990 dollars 2-years zero-coupon bond, traded currently at 955 dollars 3-years...

Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 30 percent for the next three years, with the growth rate falling off to a constant 5 percent thereafter. If the required...