Q10E The function q(x鈫�)=x鈫扵[1224]... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 8: Q10E (page 413)

The function $q (\overset{鈫�}{x}) = {\overset{鈫�}{x}}^{T} [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] \overset{鈫�}{x}$ is a quadratic form.

Short Answer

Expert verified

The given statement is TRUE.

Step by step solution

To Find TRUE or FALSE

The function is $q (\overset{鈫�}{x}) = {\overset{鈫�}{x}}^{T} [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] \overset{鈫�}{x}$ .

The given matrix is $2 脳 2$ matrix. It has two variables.

So,

role="math" localid="1664183176984" $x = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}]$ androle="math" localid="1664183149401" $x^{T} = [\begin{matrix} x_{1} & x_{2} \end{matrix}]$

Substitute these values in the given equation as follows:

role="math" localid="1664183255955" $q (\overset{鈫�}{x}) = {\overset{鈫�}{x}}^{T} [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] \overset{鈫�}{x} = [\begin{matrix} x_{1} & x_{2} \end{matrix}] [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] = [\begin{matrix} x_{1} & x_{2} \end{matrix}] [\begin{matrix} x_{1} + 2 x_{2} \\ 2 x_{1} + x_{2} \end{matrix}] = x_{1}^{2} + 2 x_{1} x_{2} + 2 x_{1} x_{2} + 4 x_{2}^{2} = x_{1}^{2} + 4 x_{1} x_{2} + 4 x_{2}^{2}$

Here, $q (x) = x_{1}^{2} + 4 x_{1} x_{2} + 4 x_{2}^{2}$ is in a quadratic form.

Thus, the given statement is TRUE.

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91影视

The function $q (\overset{鈫�}{x}) = {\overset{鈫�}{x}}^{T} [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] \overset{鈫�}{x}$ is a quadratic form.

Short Answer

Step by step solution

To Find TRUE or FALSE

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91影视

The function q(x鈫�)=x鈫�T[1224]x鈫�is a quadratic form.

Short Answer

Step by step solution

To Find TRUE or FALSE

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Decision Maths

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

The function $q (\overset{鈫�}{x}) = {\overset{鈫�}{x}}^{T} [\begin{matrix} 1 & 2 \\ 2 & 4 \end{matrix}] \overset{鈫�}{x}$ is a quadratic form.