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:

Bivalvia

Bivalvia is a class of marine and freshwater mollusks with bodies enclosed by a two-part hinged shell, including clams, oysters, mussels, and scallops.

Two Shells

Refers to bivalves, a class of aquatic mollusks with bodies enclosed by a pair of hinged shells.

Structure Labeled

A term probably meant to describe a diagram or illustration where specific parts have been marked and named to indicate their identity or function.

Function

The specific role or activity of an organ, structure, or substance in an organism or system.