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Suppose Q is the quadratic form below The minimum value of Q subject to ¹ = 1 is Q = 4. An eigenvector of A associated with eigenvalue λ = 4 is What is c equal to? An eigenvector associated with eigenvalue X = 4 is v = (0, 1, -2). The minimum value of Q, subject to = 1 is obtained at to, where: If is parallel to do and ko > 0, what must k₁ be equal to? (answer must contain at least 3 decimal places) Q = ¹A, A = 2 1 -(0) 7 = -- () = 2 1 8 2 2 5,

Suppose Q is the quadratic form below The minimum value of Q subject to ¹ = 1 is Q = 4. An eigenvector of A associated with eigenvalue λ = 4 is What is c equal to? An eigenvector associated with eigenvalue X = 4 is v = (0, 1, -2). The minimum value of Q, subject to = 1 is obtained at to, where: If is parallel to do and ko > 0, what must k₁ be equal to? (answer must contain at least 3 decimal places) Q = ¹A, A = 2 1 -(0) 7 = -- () = 2 1 8 2 2 5,

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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Suppose \( Q \) is the quadratic form below: \[ Q = \vec{x}^T A \vec{x}, \quad A = \begin{pmatrix} 5 & 2 & 1 \\ 2 & 8 & 2 \\ 1 & 2 & 5 \end{pmatrix} \] The minimum value of \( Q \) subject to \( \vec{x}^T \vec{x} = 1 \) is \( Q = 4 \). An eigenvector of \( A \) associated with eigenvalue \( \lambda = 4 \) is: \[ \vec{v} = \begin{pmatrix} 0 \\ 1 \\ c \end{pmatrix} \] What is \( c \) equal to? \[ \boxed{\phantom{insert\ text\ here}} \] An eigenvector associated with eigenvalue \( \lambda = 4 \) is \( \vec{v} = (0, 1, -2)^T \). The minimum value of \( Q \), subject to \( \vec{x}^T \vec{x} = 1 \) is obtained at \( \vec{x}_0 \), where: \[ \vec{x}_0 = \begin{pmatrix} 0 \\ k_0 \\ k_1 \end{pmatrix} \] If \( \vec{v} \) is parallel to \( \vec{x}_0 \) and \( k_0 > 0 \), what must \( k_1 \) be equal to? (Answer must contain at least 3 decimal places) \[ \boxed{\phantom{insert\ text\ here}} \]
Transcribed Image Text:Suppose \( Q \) is the quadratic form below: \[ Q = \vec{x}^T A \vec{x}, \quad A = \begin{pmatrix} 5 & 2 & 1 \\ 2 & 8 & 2 \\ 1 & 2 & 5 \end{pmatrix} \] The minimum value of \( Q \) subject to \( \vec{x}^T \vec{x} = 1 \) is \( Q = 4 \). An eigenvector of \( A \) associated with eigenvalue \( \lambda = 4 \) is: \[ \vec{v} = \begin{pmatrix} 0 \\ 1 \\ c \end{pmatrix} \] What is \( c \) equal to? \[ \boxed{\phantom{insert\ text\ here}} \] An eigenvector associated with eigenvalue \( \lambda = 4 \) is \( \vec{v} = (0, 1, -2)^T \). The minimum value of \( Q \), subject to \( \vec{x}^T \vec{x} = 1 \) is obtained at \( \vec{x}_0 \), where: \[ \vec{x}_0 = \begin{pmatrix} 0 \\ k_0 \\ k_1 \end{pmatrix} \] If \( \vec{v} \) is parallel to \( \vec{x}_0 \) and \( k_0 > 0 \), what must \( k_1 \) be equal to? (Answer must contain at least 3 decimal places) \[ \boxed{\phantom{insert\ text\ here}} \]
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