$$\text { Compute the quadratic form } x ^ { T } A x \text { for the given matrix } A \text { and vector } x \text {. }$$

question 16

Multiple Choice

$$\text { Compute the quadratic form } x ^ { T } A x \text { for the given matrix } A \text { and vector } x \text {. }$$
- $$A = \left[ \begin{array} { r r r } 4 & 8 & 0 \\8 & 1 & 2 \\0 & 2 & - 2\end{array} \right] , x = \left[ \begin{array} { l } x _ { 1 } \\x _ { 2 } \\x _ { 3 }\end{array} \right]$$

• A) \(4 x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } - 2 x _ { 3 } ^ { 2 } + 8 x _ { 1 } + 10 x _ { 2 } + 2 x _ { 3 }\)
• B) \(4 \times \frac { 2 } { 1 } + x _ { 2 } ^ { 2 } - 2 \times \frac { 2 } { 3 }\)
• C) \(4 x _ { 1 } ^ { 2 } - x _ { 2 } ^ { 2 } + 2 x _ { 3 } ^ { 2 } - 16 x _ { 1 } x _ { 2 } - 4 x _ { 2 } x _ { 3 }\)
• D) \(4 x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } - 2 x _ { 3 } ^ { 2 } + 16 x _ { 1 } x _ { 2 } + 4 x _ { 2 } x _ { 3 }\)

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Definitions:

Dimension Lines

Lines on a drawing that represent the measurement of a feature, accompanied by arrows and numerical values to denote length.

Object Lines

Thick solid lines in technical drawings that represent the visible edges of an object.

Two Millimeters

A length measurement equivalent to 0.07874 inches, often used to specify the dimension of small features in engineering and technical drawings.

Standard Unit

A predefined and universally accepted quantity used for measurement and comparison, such as meters, liters, or kilograms.