Mathematics II20755 marksNumerical: eigenvaluesThe characteristic equations
Find the eigenvalues of the matrix
Find the eigenvalues of the matrix $$\begin{bmatrix} 6 & 3 & -8 \ 0 & -2 & 0 \ 1 & 0 & -3 \end{bmatrix}$$ [5]
$$A = \begin{bmatrix} 6 & 3 & -8 \ 0 & -2 & 0 \ 1 & 0 & -3 \end{bmatrix}$$ Eigenvalues satisfy $\det(A - \lambda I) = 0$. $$A - \lambda I = \begin{bmatrix} 6-\lambda & 3 & -8 \ 0 & -2-\lambda & 0 \ 1 & 0 & -3-\lambda \end{bmatrix}$$ Row 2 has entries $0,\ (-2-\lambda),\ 0$. Only the middle te...