Step-by-Step Solution
Key Concept: Calculate the adjoint of matrix A and multiply it by matrix B, then sum the elements of the resulting vector.
Given A = [[1, 1, -1], [2, 1, 1], [3, 2, 2]]. The determinant |A| = 1(2-2) - 1(4-3) - 1(4-3) = 0 - 1 - 1 = -2. The cofactor matrix C is calculated. adj(A) = C^T. Then compute adj(A) * B where B = [[-1], [2], [3]]. Summing the elements of the resulting vector gives -1.
Correct Answer: 1