Use the Appropriate Property of Determinants from This Section to Justify

question 57

Multiple Choice

Use the appropriate property of determinants from this section to justify the true statement. $$( - 5 ) \left| \begin{array} { c c c } 3 & 1 & - 1 \\7 & 3 & 1 \\3 & 1 & 7\end{array} \right| = \left| \begin{array} { c c c } 3 & - 5 & - 1 \\7 & - 15 & 1 \\3 & - 5 & 7\end{array} \right|$$ Do not evaluate the determinants.

• 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 |.
• 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 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0.
• D) Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0.
• E) 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 |.

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Definitions:

Plate Boundaries

The edges where two tectonic plates meet, which can be sites of significant geological activity including earthquakes, volcanoes, and mountain building.

Subduction Zone

A geological region where one tectonic plate moves under another, leading to various geological phenomena, including earthquakes and volcanoes.

Destructive Earthquakes

Earthquakes that result in significant damage and loss of life, often occurring near tectonic plate boundaries where energy release is concentrated.

Red Triangle

An area notorious for its frequency of shark attacks; without context, it could also simply refer to a geometric shape in a specific color.