Make a change of variable, x = Py, that transforms the given quadratic form into a quadratic form with no cross-product term. Give P and the new quadratic form. Q(x) = 13 x + 12 x + 5 x + 20x 1x2 + 8x 1x 3 + 12x 2x 3 [2-2 1] O P= 2 1-2:25y +4y² + y² 122 [2/3-2/3 1/3] P = 2/3 1/3-2/3; 25y + 4y2 + y 1/3 2/3 2/3 [-2/3-2/3 1/3] P=-2/3 1/3-2/3:5y + 2y² + y² 1/3-2/3 2/3] [2-2 1] P= 2 1-2; y + 4y + 25 y 1 2 2
Make a change of variable, x = Py, that transforms the given quadratic form into a quadratic form with no cross-product term. Give P and the new quadratic form. Q(x) = 13 x + 12 x + 5 x + 20x 1x2 + 8x 1x 3 + 12x 2x 3 [2-2 1] O P= 2 1-2:25y +4y² + y² 122 [2/3-2/3 1/3] P = 2/3 1/3-2/3; 25y + 4y2 + y 1/3 2/3 2/3 [-2/3-2/3 1/3] P=-2/3 1/3-2/3:5y + 2y² + y² 1/3-2/3 2/3] [2-2 1] P= 2 1-2; y + 4y + 25 y 1 2 2
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 50E
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![QUESTION 12
Make a change of variable, x = Py, that transforms the given quadratic form into a quadratic form with no
cross-product term. Give P and the new quadratic form.
Q(x) = 13 x + 12 x
+5x + 20x 1x 2 + 8x 1x 3 + 12x 2x 3
2-2 17
P= 2 1-2; 25y +4y² + y²
1 2 2
[2/3-2/3 1/3]
P= 2/3 1/3-2/3; 25y + 4y2 + y²
1/3 2/3 2/3]
[-2/3-2/3 1/3]
P= -2/3 1/3-2/3; 5y + 2y2 + y²
1/3-2/3 2/3
[2-2 1
P= 2 1-2 y +4y2 + 25 y
1 2 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb8cd65e-f4bf-416e-b275-0e254fa224af%2F9350ebf3-d2be-431e-a6fc-e06e24ff7e62%2Fhvltmcr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 12
Make a change of variable, x = Py, that transforms the given quadratic form into a quadratic form with no
cross-product term. Give P and the new quadratic form.
Q(x) = 13 x + 12 x
+5x + 20x 1x 2 + 8x 1x 3 + 12x 2x 3
2-2 17
P= 2 1-2; 25y +4y² + y²
1 2 2
[2/3-2/3 1/3]
P= 2/3 1/3-2/3; 25y + 4y2 + y²
1/3 2/3 2/3]
[-2/3-2/3 1/3]
P= -2/3 1/3-2/3; 5y + 2y2 + y²
1/3-2/3 2/3
[2-2 1
P= 2 1-2 y +4y2 + 25 y
1 2 2
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