Question: If det A is close to zero, is the matrix A nearly singular? Experiment with the nearly singular 4 ( 4 matrix A in Exercise

If det A is close to zero, is the matrix A nearly singular? Experiment with the nearly singular 4 ( 4 matrix A in Exercise 9 of Section 2.3. Compute the determinants of A, 10A, and 0.1A. In contrast, compute the condition numbers of these matrices. Repeat these calculations when A is the 4 ( 4 identity matrix. Discuss your results?

Step by Step Solution

★★★★★

3.46 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

One may compute for this matrix that det A 4008 and cond A 163 T... 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)

922-L-A-E (209).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

What does it mean if a linear correlation coefcient is close to zero? Draw two scatter diagrams for which the linear correlation coefcient is close to zero.

(a) Give an example to show that if A can be partitioned as where P, Q, R, and S are all square, then it is not necessarily true that det A = (det P) (det S) - (det Q) (det R) (b) Assume that A is...

True or false: If true, explain why. If false, give an explicit counterexample. (a) If det 0 then A-l exists. (b) det(2A) = 2 det A. (c) det(A -(- B) = det A + det B. (d) (e) (f) det[(A + B)(A - B)]...

If det A is close to zero, is the matrix A nearly singular? Experiment with the nearly singular 4 x 4 matrix Compute the determinants of A, 10A, and 0.1A. In contrast, compute the condition numbers...

Eigenvalues and Conditioning A singular matrix must have a zero eigenvalue, but must a nearly singular matrix have a "small" eigenvalue? Consider a matrix of the form 6 points 0 0 -1 1 0 00 -1 0 00 0...

SOLVE EXERCISE 16.1 and 16.2 please. show code and ideally use matlab. or, componentwise, as ard solve the system of equations Ax = b using the three alternative methods i) x = A-lb, (the inverse A-1...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

The best definition for nonparametric statistics I can think of is when data does not fit inside the normal parameters of a normal distribution, it calls for the use of this statistical method....

MATLAB Project d goldhill.jpg krusty.jpg kface.jpg goldengate.jpg toucan.jpg barbara.jpg track.jpg bridge.jpg 4 MATLAB Project In this project you will be asked to analyze digital images using the...

Solve for x without using a calculating utility. Use the natural logarithm anywhere that logarithms are needed. 3 = 2 5-2x = 3 3e-2x = 5 2ex = 7 et - 2xet = 0 xe* +2e=0 Solve e-2-3e* = -2 for x...

Evaluate this statement: Current antidiscrimination statutes require employers to hire people who are unqualified for their jobs.

16. LO 7 To control pollution, assume that your government tightens regulations on one hand and provides a lump-sum subsidy (S) to irms that use clean technology on the other. Now, a representative...

You are asked to estimate the coefficients in a linear discriminant function. You do not have a computer program for this. All you have is a program for multiple regression analysis. How will you...

Mention an appropriate theorem in your explanation. Suppose that A is a square matrix such that det A 3 = 0. Explain why A cannot be invertible.

A and B are n x n matrices. Mark each statement True or False (T/F). Justify each answer. (T/F) det A -1 = (-1) det A.

Test the inverse formula of Theorem 8 for a random 4 x 4 matrix A. Use your matrix program to compute the cofac- tors of the 3 x 3 submatrices, construct the adjugate, andset B= (adj A)/(det A). Then...

-212 > Assignments > Chapter 11 - Problem Solving Chapter 11 - Problem Solving Submit Assignment Due Saturday by 11:59pm Points 15 Submitting a text entry box Available Feb 7 at 12am - Feb 13 at...

Using the 2012 financial statements for DRE Corporation and this additional information, prepare a pro forma income statement and balance sheet for the year 2013. Determine the discretionary...

1.An Ipsos poll found that 452 out of 1005 people believe that UFOs exist and have visited the Earth. a.Find the 99% confidence interval of this distribution. b.What minimum sample size would be...