Consider the following quadratic form on R²:43 2 57 2+-x7²25-X₂225Q(x)=[₁]=48a) Determine whether Q is positive or negative (semi)definite.b) Find a change of variables x = Py that converts Q to a form with no cross-product terms.c) write Q in terms of the new variables y 1 and y2.In your formula, write 'y_1' and 'y_2' for y₁ and y2. Use the square root symbol 'V' where needed to give an exact value foryour answer.[00₁]0 0 100 42+.a) The quadratic form is < Select an answer >< Select an answer >c) Q(x) = 025-X1X2Positive DefiniteNegative DefinitePositive SemidefiniteNegative SemidefiniteIndefinite

Answered: Image /qna-images/answer/fd21a2da-45cd-47f2-a552-1deee1b38305.jpg

Consider the following quadratic form on R²: Q(x) = ²x₂²¹ +27x₂² +48x2x2 43 2 57 -x1 25 25 25 a) Determine whether Q is positive or negative (semi)definite. b) Find a change of variables x = Py that converts Q to a form with no cross-product terms. c) write Q in terms of the new variables y/1 and 1/2- In your formula, write 'y_1' and 'y_2' for 1₁ and 12. Use the square root symbol '√' where needed to give an exact value for your answer. a) The quadratic form is < Select an answer > < Select an answer > Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinite [001] 004₂ b) - c) Q(x) = 0

Consider the following quadratic form on R²: Q(x) = ²x₂²¹ +27x₂² +48x2x2 43 2 57 -x1 25 25 25 a) Determine whether Q is positive or negative (semi)definite. b) Find a change of variables x = Py that converts Q to a form with no cross-product terms. c) write Q in terms of the new variables y/1 and 1/2- In your formula, write 'y_1' and 'y_2' for 1₁ and 12. Use the square root symbol '√' where needed to give an exact value for your answer. a) The quadratic form is < Select an answer > < Select an answer > Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinite [001] 004₂ b) - c) Q(x) = 0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 7DE

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