Refer a friend and earn $50 when they subscribe to an annual planRefer Now
Get the answer to your homework problem.
Try Numerade Free for 30 Days
Like
Report
Make a change of variable, $\mathbf{x}=P \mathbf{y},$ that transforms the quadratic form $x_{1}^{2}+10 x_{1} x_{2}+x_{2}^{2}$ into a quadratic form with no cross-product term. Give $P$ and the new quadratic form.
$6 y_{1}^{2}-4 y_{2}^{2}$
Algebra
Chapter 7
Symmetric Matrices and Quadratic Forms
Section 2
Quadratic Forms
Introduction to Matrices
McMaster University
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
Lectures
01:32
In mathematics, the absolu…
01:11
03:24
In Exercises 1 and $2,$ fi…
03:40
05:52
Classify the quadratic for…
02:35
02:33
07:50
03:15
03:01
05:22
04:07
Okay, so you miss program, we have ah nominal excellence group last 10 x one x two US x two square eso This party nominal corresponds to a car genetic form with the symmetric men shakes 11 and the 55 I'm 61 x two. So we are looking for We are looking for coordinated change. I do you find you find ah man checks p such that xy cost of p Thomas. Why? Where? Why he closed to just why one and white you. So we are looking for this kind off transformation. So your little figure out was the P we denote this image of mentions by and Toronto find are the item value and Aiken vector off a. This is the real symmetric metric, so we can always figure out these things. So the characteristic equation it will be the determinant off a mine. Islam die. In this case, you will be one minus Lambda Square minus 25 equals zero, which gives us Lambda wine cause the six in the lamb that week was to minus four. So for Lambda One, it was 26 a miner's six I equals two minus 55 minus, um, five minus five. So corresponds to and I convict early. One equals 21 over. Route off. Two times 11 We use a normalized again. Victor in the phylum 0.2 equals two minus four a minus minus four I because to oh equals 25555 And they corresponds to another Eigen vector, which is one Have one of the root off to one minus one or we can use minus one. It doesn't matter. So the metrics p we are looking for will be a combination off these two column vectors with this, um, Magic p and this, um, transformation. We were have x transpose times eight times. Eggs equals to just plug in this expression we have. Why chills post times p transpose times eight times p times. Why? And, uh, this matrix multiplication gives us, um, a diagonal men tricks. And with Agam Agam variables on the diagonal injuries. So we have my r six and the minus 400 times why? And in the end, away have six y one square proud miners four white to square. This know of crows productor With this transformation
View More Answers From This Book
Find Another Textbook
In mathematics, the absolute value or modulus |x| of a real number x is its …
In Exercises 1 and $2,$ find the change of variable $\mathbf{x}=P \mathbf{y}…
Classify the quadratic forms in Exercises $9-18 .$ Then make a change of var…
04:33
Let $A$ be an $m \times n$ matrix and, given $\mathbf{b}$ in $\mathbb{R}^{m}…
04:45
In Exercises 21 and $22,$ matrices are $n \times n$ and vectors are in $\mat…
03:12
Find the characteristic polynomial and the eigenvalues of the matrices in Ex…
04:21
Determine which of the matrices in Exercises $7-12$ are orthogonal. If ortho…
02:42
06:28
Exercises $3-8$ refer to $\mathbb{P}_{2}$ with the inner product given by ev…
02:12
Suppose $\mathbf{y}$ is orthogonal to $\mathbf{u}$ and $\mathbf{v} .$ Show t…
02:15
For the matrices in Exercises $15-17$ , list the eigenvalues, repeated accor…
00:45
Exercises $9-14$ require techniques from Section $3.1 .$ Find the characteri…
01:55
Find the matrix of the quadratic form. Assume $\mathbf{x}$ is in $\mathbb{R}…
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.