Discussion
Find the determinant of matrix
\[ A = \begin{bmatrix} 4 & 6 & 1 \\ 2 & 5 & 2 \\ 9 & 0 & 4 \end{bmatrix}. \]
Answer: D
The determinant is 95.
Expand along the first row:
\[ \begin{aligned} |A| &= 4(5 \times 4 - 2 \times 0) \\ &\quad - 6(2 \times 4 - 2 \times 9) \\ &\quad + 1(2 \times 0 - 5 \times 9) \\ &= 80 + 60 - 45 = 95 \end{aligned} \]
The middle term is \(-6 \times (8 - 18) = +60\). Taking it as \(-60\) gives \(80 - 60 - 45 = -25\), and stopping after the first term gives 80, one of the distractors.
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