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Let A1 = det|a b c; b c a; c a b| ≠ 0 and A2 = det|a+2b b+3c c+4a; b+2c c+3a a+4b; c+2a a+3b b+4c|. Find the value of A2/A1.
- 17
- 25
- 30
- 10
Correct answer: 25
Solution
Using multilinearity of the determinant, only two non-zero terms survive: det[C1|C2|C3] = A1 and 2*3*4*det[C2|C3|C1] = 24A1 (since the cyclic permutation C1->C2->C3->C1 has even parity, det[C2|C3|C1] = +A1). Hence A2 = 25A1.
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