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If a0, a1, a2, a3, a4 are in arithmetic progression with common difference d (d ≠ 0, ±1), find the value of the 3x3 determinant with rows [a1*a2, a1, a0], [a2*a3, a2, a1], [a3*a4, a3, a2].
- 2d⁴
- 2d³
- 2d²
- 4d⁴
Correct answer: 2d⁴
Solution
Let a0=a. After R2-R1 and R3-R2, the third row becomes [2d², 0, 0]. Expanding along this row: det = 2d² * minor = 2d² * (a1*d - a0*d) = 2d² * d² = 2d⁴.
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