Use the Appropriate Property of Determinants from This Section to Justify

question 191

Short Answer

Use the appropriate property of determinants from this section to justify the true statement. $$\left| \begin{array} { c c c } 10 & 2 & 3 \\5 & - 1 & 6 \\20 & - 4 & 12\end{array} \right| = 15 \left| \begin{array} { c c c } 2 & 2 & 1 \\1 & - 1 & 2 \\4 & - 4 & 4\end{array} \right| = 60 \left| \begin{array} { c c c } 2 & 2 & 1 \\1 & - 1 & 2 \\1 & - 1 & 1\end{array} \right|$$ 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.

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