Make the change of variable, x Py, that transforms the quadratic form x 1 2 12x 1 x 2 x 2 2 into a quadratic form with no cross product terms Give P and the new quadratic form

Question: Make the change of variable, x = Py, that transforms the quadratic form x 1 2 + 12x 1 x 2 + x 2 2

Make the change of variable, x = Py, that transforms the quadratic form x₁² + 12x₁x₂ + x₂²into a quadratic form with no cross-product terms. Give P and the new quadratic form.

Step by Step Solution

★★★★★

3.48 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

15 The matrix of the quadratic form is A 4 3 The eigenvalues of A are ... 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 Linear Algebra And Its Applications Questions!

Let A be the matrix of the quadratic form It can be shown that the eigenvalues of A are 1, 7, and 13. Find an orthogonal matrix P such that the change of variable x = Py transforms x T Ax into a...

Find the change of variable x = Py that transforms the quadratic form x T Ax into y T Dy as shown. 5x + 5x + 3x3 + 10x1x2 + 4x1x3+4x2x3 = 11y+2y

Find the change of variable x = Py that transforms the quadratic form x T Ax into y T Dy as shown. 5x + 4x + 3x + 4x1x2 + 4x2x3 = 7y + 4y + y

Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. - x 7 + 12 x 1 X2 - X...

Make a change of variable, x = Py, that transforms the quadratic form 4x , + 18x1X2 + 4x2 into a quadratic form with no cross-product term. Give P and the new quadratic form. Which of the following...

Please answer both parts point(s) possible Make a change of variable, x = Py, that transforms the quadratic form 3x, + 10x1X2 + 3x2 into a quadratic form with no cross-product term. Give P and the...

Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. - 9x1 - - 12 x1X2 . ....

1. Find the matrix of the quadratic form 3r; - 4142 + 52?; assume x is in R2. 2. Classify the quadratic form 4r, - 41142 + 41,. Then make a change of variable x = Py that transforms the quadratic...

1. Find the change of variable x = Py that transforms the quadratic form x Ax into y Dy as shown: 517 + 623+ 713 + 4.1 12 - 4.213 - 947 + 692 + 392 2. Let Q(x) = 5x7 + 623 + 713 + 4102 - 40213 Find...

We rank support departments when using the step-down method. Alternate ranking criteria include department size, number of other departments serviced, and arbitrary ranking. Which method will usually...

Determine the Chit Lower Triangular unque LU-decomponition of the matrix- matix L in the -3 A: 5 - IS -3 15-9 10 %3D 3 %3D -3 155 3 2. Ls 3. L= 4. L= 5 -5 5. L= 5-3 1 6. L- 5 3

3. Name three metals suitable for use as sacrificial anodes to protect the steel hull of a ship from rusting.

Think about your own online interactions. When have you engaged in hyperpersonal relationships? When have you used warranting to determine if anothers online persona was authentic?

If you took repeated samples of size 100 and constructed a 95% confidence interval for the population proportion who would shop at the store because of the coat sale from each sample, what percentage...

If you took repeated samples of size 100 and constructed a 99% confidence interval for the population proportion who would shop at the store because of the coat sale from each sample, what percentage...

Suppose we have a collection of the heights of all students at your college. Each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence...

! Required information [The following information applies to the questions displayed below) In its first month of operations, Literacy for the Illiterate opened a new bookstore and bought merchandise...

Total Stockholders Equity $15,830,000 On August 1, 2018, the board of directors of Howell declared a 15% stock dividend on common stock, to be distributed on September 15th. The market price of...

Please show detailed answers. b. Prepare the post-closing trial balance as of December 31, 2015 c. Prepare the classified balance sheet at December 31, 2015. The alphabetical listing below includes...