Find the Matrix of the Quadratic Form $$6 x _ { 1 } x _ { 2 } - 18 x _ { 1 } x _ { 3 } + 18 x _ { 2 } x _ { 3 }$$

question 8

Multiple Choice

Find the matrix of the quadratic form.
- $$6 x _ { 1 } x _ { 2 } - 18 x _ { 1 } x _ { 3 } + 18 x _ { 2 } x _ { 3 }$$

• A)
• \(\left[ \begin{array} { r r r } 0 & 6 & - 18 \\ 6 & 0 & 18 \\ - 18 & 18 & 0 \end{array} \right]\)
• B)
• \(\left[\begin{array}{rrr}
• 3 & 0 & 0 \\
• 0 & -9 & 0 \\
• 0 & 0 & 9
• \end{array}\right]\)
• C)
• \(\left[\begin{array}{rrr}
• 0 & 3 & -9 \\
• 3 & 0 & 9 \\
• -9 & 9 & 0
• \end{array}\right]\)
• D)
• \[\left[ \begin{array} { r r r }
• 1 & 3 & - 9 \\
• 3 & 1 & 9 \\
• - 9 & 9 & 1
• \end{array} \right]\]

---

Definitions:

Population Growth

The increase in the number of individuals in a population due to births outpacing deaths or through migration.

Demographic Data

Information collected about the characteristics of human populations, such as age, gender, income, and education.

Crude Birth Rate

The rate of live births per thousand inhabitants in a population for a specified year.

Crude Death Rate

A measure of the number of deaths in a given population, scaled to the size of that population, per unit of time.