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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following quadratic form on R²: 43 2 57 2 + -x7² 25 -X₂ 2 25 Q(x) = [₁] = 48 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 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 for your answer. [00₁] 0 0 1 00 42 +. a) The quadratic form is < Select an answer > < Select an answer > c) Q(x) = 0 25 -X1X2 Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinite
Transcribed Image Text:Consider the following quadratic form on R²: 43 2 57 2 + -x7² 25 -X₂ 2 25 Q(x) = [₁] = 48 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 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 for your answer. [00₁] 0 0 1 00 42 +. a) The quadratic form is < Select an answer > < Select an answer > c) Q(x) = 0 25 -X1X2 Positive Definite Negative Definite Positive Semidefinite Negative Semidefinite Indefinite
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