Give a Step-By-Step Explanation of How to Evaluate the Determinant $$\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|$$

question 74

Multiple Choice

Give a step-by-step explanation of how to evaluate the determinant. Match sequence of steps. $$\left| \begin{array} { c c c } 5 & 0 & 4 \\1 & - 4 & 6 \\7 & 0 & 9\end{array} \right|$$
-Second step

• A) \(\left| \begin{array} { c c c }
• 5 & 0 & 4 \\
• 1 & - 4 & 6 \\
• 7 & 0 & 9
• \end{array} \right| = ( 0 ) ( - 1 ) ^ { 2 + 1 } \left| \begin{array} { l l }
• 1 & 6 \\
• 7 & 9
• \end{array} \right| + ( - 4 ) ( - 1 ) ^ { 2 + 2 } \left| \begin{array} { l l }
• 5 & 4 \\
• 7 & 9
• \end{array} \right| + ( 0 ) ( - 1 ) ^ { 2 + 3 } \left| \begin{array} { l l }
• 5 & 4 \\
• 1 & 6
• \end{array} \right|\)
• B) \(\left| \begin{array} { c c c }
• 5 & 0 & 4 \\
• 1 & - 4 & 6 \\
• 7 & 0 & 9
• \end{array} \right| = ( 0 ) ( - 1 ) ( - 33 ) + ( - 4 ) ( 1 ) ( 17 ) + ( 0 ) ( - 1 ) ( 26 )\)
• C) \(\left| \begin{array} { c c c }
• 5 & 0 & 4 \\
• 1 & - 4 & 6 \\
• 7 & 0 & 9
• \end{array} \right| = 0 - 68 + 0 = - 68\)

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