Evaluate the Determinant of the Given Matrix and State Whether $$A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]$$

question 14

Multiple Choice

Evaluate the determinant of the given matrix and state whether the matrix is invertible.
- $$A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]$$

• A) 648 , No
• B) \(648 , \mathrm { Yes }\)
• C) \(1,026 , \mathrm { Yes }\)
• D) \(1,026 , \mathrm { No }\)

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Definitions:

Replacement Rate

The total fertility rate necessary to offset deaths in a country and thereby keep the size of its population constant (without relying on immigration). For most countries, a total fertility rate of about 2.1 births per woman per lifetime.

Per-Capita Consumption

The average consumption of a good or service per person within a particular population or area.

Total Fertility Rate

A demographic measure that estimates the average number of children a woman will have over her childbearing years, given current birth rates.

Falling Birthrates

A demographic trend characterized by a decrease in the birth rate over a period, often leading to shifts in national and global population dynamics.