Suppose that the eigenvalues of matrix A are 1,2,4. The determinant of (A− I…
2016
Suppose that the eigenvalues of matrix A are 1,2,4. The determinant of (A− I )T is _____________ .
Attempted by 105 students.
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Correct answer: 0.124 to 0.126
Key idea: the determinant of a matrix equals the product of its eigenvalues; the determinant of an inverse is the reciprocal of the determinant; and the determinant of a transpose equals the determinant.
Compute the determinant of A by multiplying its eigenvalues: 1 × 2 × 4 = 8.
The determinant of A inverse is the reciprocal: 1 / 8 = 1/8.
The determinant of the transpose equals the determinant, so the determinant of (A inverse) transpose is also 1/8.
Final answer: 1/8 = 0.125