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Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable substitution x = Py that transforms the quadratic form to one with no cross-product terms. (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x² + 4x² + 4x3 + 4x² +8x1X2 +8X3X4 − 6X1X4 + 6X2X3. 1.2 Q₂(x) = 2x² + 2x² - 6x1x2 - 6x13 - 6x1x4 – 6x2x3 - 6x2*4 - 2x3x4-

Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable substitution x = Py that transforms the quadratic form to one with no cross-product terms. (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x² + 4x² + 4x3 + 4x² +8x1X2 +8X3X4 − 6X1X4 + 6X2X3. 1.2 Q₂(x) = 2x² + 2x² - 6x1x2 - 6x13 - 6x1x4 – 6x2x3 - 6x2*4 - 2x3x4-

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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Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: = (a) Make a change-of-variable substitution x form to one with no cross-product terms. Py that transforms the quadratic (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x² + 4x² + 4x² + 4x² +8X1X2 +8X3x4 - 6x₁x4 + 6x₂x3. 1.2 Q2₂(x) = 2x² + 2x2 - 6x1x2 - 6x1x3 - 6x1x4 - 6x2x3 - 6x2x4 - 21314-
Transcribed Image Text:Question 1 Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: = (a) Make a change-of-variable substitution x form to one with no cross-product terms. Py that transforms the quadratic (b) Write down the new quadratic form. (c) Classify the quadratic form as positive definite, negative definite or indefi- nite. 1.1 Q₁(x) = 4x² + 4x² + 4x² + 4x² +8X1X2 +8X3x4 - 6x₁x4 + 6x₂x3. 1.2 Q2₂(x) = 2x² + 2x2 - 6x1x2 - 6x1x3 - 6x1x4 - 6x2x3 - 6x2x4 - 21314-
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