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A determinant A has rows (a b c), (p q r), (x y z) and A = 6. Define B as the determinant with rows (p+x q+y r+z), (a+x b+y c+z), (a+p b+q c+r). Find B.
- B = 6
- B = -6
- B = 12
- B = -12
Correct answer: B = 12
Solution
Expanding the sum-of-rows determinant leaves two copies of A (after row permutations), giving B = 2A = 12.
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