allerySolve: x + y + z = 6, 2x + y - z = 1, x - y + z = 2. Determinant of coefficient matrix:
A12
B-6 (det of [[1,1,1],[2,1,-1],[1,-1,1]])
C6
D0
Answer & Solution
Correct answer: B. -6 (det of [[1,1,1],[2,1,-1],[1,-1,1]])
Expanding along row 1: 1×(1×1 - (-1)(-1)) - 1×(2×1 - (-1)×1) + 1×(2×(-1) - 1×1) = 1×(1-1) - 1×(2+1) + 1×(-2-1) = 0 - 3 - 3 = -6.
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