Assume A ∈ ℝ^4 has eigenvalues 1, 2, 3. Find (52 |A| 5^0)^999 where |A| denotes determinant. (Hint: Note A has distinct eigenvalues and can be put into an eigendecomposed form VAV^-1 such that |A| = |VAV^-1| = |V| |A| |V^-1|.)
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Now, we want to find the determinant of (5I - A). Using the hint, we can rewrite this as: |5I - A| = |5VIV^{-1} - VAV^{-1}| = |V(5I - A)V^{-1}|. Since the determinant of a product of matrices is the product of their determinants, we have: |5I - A| = |V||5I - Show more…
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