Let be a matrix with eigenvalues , , and . What is the determinant of the matrix ?
Answer and explanation
Correct answer: C. 7
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- Step 1: By the spectral mapping theorem, if is an eigenvalue of , then for polynomial , the corresponding eigenvalue of is .
- Step 2: Compute the eigenvalues of corresponding to , , and :
- Step 3: The determinant of a matrix equals the product of its eigenvalues: .
Answer
7.
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