4. A quadratic form Q in the components ₁,...,n of a vector = [₁,...,n] with symmetric coefficient matrix A = (a¡j)1≤ij≤n is defined to be n Q(x) := a¹ Añ = ΣΣaijXiTj. i=1 jul Use THREE methods to determine whether the following quadratic forms in three variables is positive or negative definite or semidefinite, or indefinite. Q(x) = 6x² + 6x2 + 5x² - 4x1x2.
4. A quadratic form Q in the components ₁,...,n of a vector = [₁,...,n] with symmetric coefficient matrix A = (a¡j)1≤ij≤n is defined to be n Q(x) := a¹ Añ = ΣΣaijXiTj. i=1 jul Use THREE methods to determine whether the following quadratic forms in three variables is positive or negative definite or semidefinite, or indefinite. Q(x) = 6x² + 6x2 + 5x² - 4x1x2.
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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![4. A quadratic form in the components ₁,...,n of a vector 7= [₁,...,n]
with symmetric coefficient matrix A = (aij)<i.j≤n is defined to be
n n
Q(x) = a¹ At=ΣajjXiTj.
i=1 j=1
Use THREE methods to determine whether the following quadratic forms in
three variables is positive or negative definite or semidefinite, or indefinite.
Q(x) = 6x² + 6x² + 5x² - 4x1x2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a6c81fb-8e60-497d-8258-bbf9a213fe79%2F606a0721-34fc-480b-be63-f9e00788293f%2Fehpq08m_processed.png&w=3840&q=75)
Transcribed Image Text:4. A quadratic form in the components ₁,...,n of a vector 7= [₁,...,n]
with symmetric coefficient matrix A = (aij)<i.j≤n is defined to be
n n
Q(x) = a¹ At=ΣajjXiTj.
i=1 j=1
Use THREE methods to determine whether the following quadratic forms in
three variables is positive or negative definite or semidefinite, or indefinite.
Q(x) = 6x² + 6x² + 5x² - 4x1x2.
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