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

question 12

Multiple Choice

Use the properties of determinants to find the value of the second determinant, given the value of the first.
- $$\left| \begin{array} { c c c } x & y & z \\u & v & w \\1 & - 3 & - 4\end{array} \right| = 62 \left| \begin{array} { c c c } 1 & - 3 & - 4 \\3 u & 3 v & 3 w \\x - 1 & y + 3 & z + 4\end{array} \right| = ?$$

• A) 186
• B) -186
• C) 62
• D) -62

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Definitions:

Stepparents

Individuals who are married to a biological parent of a child and may take on parental responsibilities without being the child’s biological parent.

Nuclear Families

A family group consisting of two parents and their children (biological or adopted), considered a basic social unit.

Single-mother Households

Family units headed by a female parent without the presence of a spouse or male partner.

Single-father Households

Living arrangements where one man is the primary or sole caregiver and guardian for one or more children.