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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