The characteristic equation of a matrix $A$ is $\lambda^3 - 5\lambda^2 - 3\lambda + 2 = 0$ then $|\text{adj}A| = $
Step-by-Step Solution
Key Concept: The eigenvalues of matrix A are roots of the characteristic equation. Since det(A) equals the product of eigenvalues, substitute λ=0 into the characteristic polynomial to find |A|. Then apply the formula |adj(A)| = |A|^(n-1) for an n×n matrix.
Using the property that $\text{adj}(A) = |A| \cdot A^{-1}$, we have $|\text{adj}(A)| = |A|^{n-1}$ for an $n \times n$ matrix. For $n = 3$ and $|A| = -2$, we get $|\text{adj}(A)| = (-2)^2 = 4$.
Correct Answer: 4