Use the Appropriate Property of Determinants from This Section to Justify

question 198

Multiple Choice

Use the appropriate property of determinants from this section to justify the true statement. $$\left| \begin{array} { c c c } 12 & 3 & 3 \\4 & - 1 & 9 \\20 & - 5 & 15\end{array} \right| = 12 \left| \begin{array} { c c c } 3 & 3 & 1 \\1 & - 1 & 3 \\5 & - 5 & 5\end{array} \right| = 60 \left| \begin{array} { c c c } 3 & 3 & 1 \\1 & - 1 & 3 \\1 & - 1 & 1\end{array} \right|$$ Do not evaluate the determinants.

• 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 |.
• B) Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns), then | B | = \(-\) | A |.
• C) 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 |.
• D) Property number 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0.
• E) Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0.

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Definitions:

Test Validity

The degree to which a test accurately measures what it is intended to measure, ensuring that the test results are relevant and meaningful for its purpose.

Test Reliability

The degree to which an assessment tool produces stable and consistent results over repeated applications.

Hostile Work Environment

A form of sexual harassment when an employee experiences workplace harassment such as provocative pictures that make the environment an offensive place to work.

Quid Pro Quo

A form of sexual harassment that means “in exchange for this, I’ll give you that.”