💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Like

Report

[M] Construct a random integer-valued $4 \times 4$ matrix $A,$ and verify that $A$ and $A^{T}$ have the same characteristic polynomial (the same eigenvalues with the same multiplicies). Do $A$ and $A^{T}$ have the same eigenvectors? Make the same analysis of a $5 \times 5$ matrix. Report the matrices and your conclusions.

See solution

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 2

The Characteristic Equation

Vectors

Johns Hopkins University

Missouri State University

Campbell University

Harvey Mudd College

Lectures

02:56

In mathematics, a vector (…

06:36

01:39

[M] Construct a random $4 …

01:24

For a randomly generated $…

03:51

Determine the multiplicity…

03:24

00:51

Use some form of technolog…

02:53

20:00

Let $A=\left[\begin{array}…

01:52

Determine the eigenvalues …

02:44

Okay. So in this example, we want to see how these four transformations will affect the determines off A when we use random former for matrices. So I created a love another program here, where we will generate random matrices depending on this shape. Yeah, so if you want to use it on five by five and 656 matrix Just changed history. Five comma five and six. Common six. Then what this will do is that this will find the ratio between eight transfers on A. So it's going to wipe transfers and eight to the ratio between negative, eh? And eh, The ratio between two. A two and ratio of 10 8 to a and then everything worry about what's called us. But that's what it does. So what you find out is that the determined a transpose should be equal to two determinant off, eh? Determined off negative. A is equal to negative one times by and determines all, eh? So here I'm just gonna make a random a general n by N matrix. And then this one will be true to the end determinants. Oh, hey, this is 10 to the end tournaments away and in this case because this is for for so many years, for this will just be one to the end. So it's gonna be equal to determine off A is going to be too to the form, so you'll get 16 and this is tentative. Fall and you'll you'll see this when you perform this program.

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

[M] Construct a random $4 \times 4$ matrix $A$ with integer entries between …

For a randomly generated $5 \times 5$ matrix, verify that $\operatorname{det…

Determine the multiplicity of each eigenvalue and a basis for each eigenspac…

Use some form of technology to determine the eigenvalues and a basis for eac…

Let $A=\left[\begin{array}{rrr}{4} & {-1} & {-1} \\ {-1} & {4} &…

Determine the eigenvalues of the given matrix $A$. That is, determine the sc…

02:03

In Exercises $13-20,$ find an invertible matrix $P$ and a matrix $C$ of the …

00:47

Compute the quantities in Exercises $1-8$ using the vectors$$\mathbf…

02:47

Suppose $A$ and $B$ are both orthogonally diagonalizable and $A B=B A .$ Exp…

03:42

Exercises 23 and 24 show how to classify a quadratic form $Q(\mathbf{x})=\ma…

01:46

Suppose $\mu$ is an eigenvalue of the $B$ in Exercise $15,$ and that $\mathb…

01:41

The space is $C[0,2 \pi]$ with the inner product $(6)$.Suppose the first…

05:51

Find an orthonormal basis of the subspace spanned by the vectors in Exercise…

04:14

Involve a design matrix $X$ with two or more columns and a least-squares sol…

01:20

Determine which of the matrices in Exercises $1-6$ are symmetric. $$…

03:28

Use the inner product axioms and other results of this section to verify the…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.