Use the Properties of Determinants to Find the Value of the Second

question 1

Multiple Choice

Use the properties of determinants to find the value of the second determinant, given the value of the first.
- $$\left| \begin{array} { c c c } x & y & z \\u & v & w \\1 & - 3 & 4\end{array} \right| = - 138 \left| \begin{array} { c c c } x & y & z \\u & v & w \\2 & - 6 & 8\end{array} \right| = ?$$ $$\begin{array} { c c c } x & y & z \\a & v & w \\1 & - 3 & 4\end{array} | = - 138 | \begin{array} { c c c } x & y & z \\u & v & w \\2 & - 6 & 8\end{array} \mid = ?$$

• A) -276
• B) -138
• C) 276
• D) 138

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Definitions:

Altruism

A selfless concern for the well-being of others, often manifesting as unselfish acts or behaviors.

Least Altruistic

Describes individuals or actions that show the smallest degree of concern for the welfare of others, often prioritizing self-interest.

Individualist Cultures

Individualist cultures prioritize the rights and importance of the individual over the collective, emphasizing personal freedom, self-expression, and independence.

Personal Goals

Individual objectives set by a person, aiming to achieve desired outcomes or accomplishments in various aspects of their life, such as career, education, health, or personal relationships.