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Let D1 be the determinant of the matrix [[a, b, a+b], [c, d, c+d], [a, b, a-b]] and D2 the determinant of [[a, c, a+c], [b, d, b+d], [a, c, a+b+c]]. With b != 0 and ad != bc, find the value of D1/D2.

1. -2
2. 0
3. -2b
4. 2b

Correct answer: -2

Solution

Column operations reduce D1 to -2b*(ad - bc) and D2 to b*(ad - bc), so D1/D2 = -2.

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