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The first row of a 3x3 matrix A is [1, 3, 2]. The adjugate of A is given by adj(A) = [[-2, 4, alpha], [-1, 2, 1], [3*alpha, -5, -2]]. Determine a possible value of det(A).
- 1
- 2
- -1
- -2
Correct answer: 1
Solution
Multiplying the first row [1,3,2] by each column of adj(A) and equating to det(A)*I yields alpha = 1 from the condition that the (1,3) entry equals 0, and then det(A) = 6*alpha - 5 = 1.
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