Factor the matrix A into a product XDX-1 where D is diagonal. A = (1 2 -1 2 4 -2 3 6 -3)
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The characteristic equation is det(A - λI) = 0 = det\(\begin{bmatrix} 1-\lambda & 2 & 3 \\ 2 & 4-\lambda & 6 \\ -1 & -2 & -\lambda \end{bmatrix}\) = 0 Expanding the determinant, we get: = (1-λ)((4-λ)(-λ) - (-2)(6)) - 2(2(-λ) - (-1)(6)) + 3(2(-2) - 4(-1)) = Show more…
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