5. (15 pts - Eigenvalues and eigenvectors) (Show your work!) Given $A = \begin{bmatrix} 1 & -2 \ 1 & 4 \end{bmatrix}$ (a) Find the two eigenvalues of $A$. (b) Find the unit eigenvector corresponding to the eigenvalue with the larger value.
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A = [1 -2] The characteristic equation is: det(A - λI) = det([1 -2] - λ[1 0]) = det([1-λ -2] [0 1-λ]) = (1-λ)(1-λ) - (-2)(0) = (1-λ)^2 Setting the characteristic equation equal to zero: (1-λ)^2 = 0 Solving Show more…
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