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

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) \(4 x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } - 2 x _ { 3 } ^ { 2 } + 16 x _ { 1 } x _ { 2 } + 4 x _ { 2 } x _ { 3 }\)

---

Definitions:

Absolute Purchasing Power Parity

A theory that in the long term, exchange rates should move towards rates that would equalize the prices of an identical basket of goods in any two countries.

Canadian Dollar

The currency of Canada, often represented by the symbol CAD.

British Pound

The recognized monetary unit of the United Kingdom, also referred to as GBP (Great Britain Pound).

London Interbank Offer Rate

An interest rate average calculated from estimates submitted by the leading banks in London, used as a benchmark for lending rates worldwide.