Question
Find the eigenvalues and eigenvectors of the following matrices:$$\left(\begin{array}{rrr}4 & 0 & 2 \\-6 & 1 & -4 \\-6 & 0 & -3\end{array}\right)$$
Step 1
- Compute det(A − λI) for A = [[4,0,2],[-6,1,-4],[-6,0,-3]]: det(A−λI) = (4−λ)det([[1−λ,−4],[0,−3−λ]]) + 2 det([[-6,1−λ],[-6,0]]) = (4−λ)(−(1−λ)(λ+3)) + 12(1−λ) = (1−λ)[−(4−λ)(λ+3) + 12] = (1−λ)[λ(λ−1)] = −λ(λ−1)^2. - Show more…
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