Use the Appropriate Property of Determinants from This Section to Justify

question 148

Short Answer

Use the appropriate property of determinants from this section to justify the true statement. $$\left| \begin{array} { c c c } 7 & 9 & 15 \\8 & - 12 & 4 \\7 & 6 & - 1\end{array} \right| = - \left| \begin{array} { c c c } 7 & 15 & 9 \\8 & 4 & - 12 \\7 & - 1 & 6\end{array} \right|$$ Do not evaluate the determinants. Property number 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0. Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns), then | B | = $-$ | A |. Property number 3: If square matrix B is obtained from square matrix A by multiplying each element of any row (or column) of A by some real number k , then | B | = k | A |. Property number 4: If square matrix B is obtained from square matrix A by adding k times a row (or column) of A to another row (or column) of A , then | B | = | A |. Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0. Enter property number only.

---

Definitions:

College Degree

An academic certification awarded by colleges or universities upon completion of a course of study, indicating the holder's expertise in a specific field.

Public Assistance

Government programs designed to provide financial aid, food, medical care, and housing to individuals and families with low income.

Emotional Problems

Issues related to an individual's emotional well-being, such as depression, anxiety, or stress that can impact daily functioning.

New Found Freedom

A sense of liberty and independence discovered or experienced for the first time, often after a period of restriction.