So the Eigenvalues are −1, 2 and 8 Subsection 5.1.1 Eigenvalues and Eigenvectors. :2/x2: Separate into eigenvectors:8:2 D x1 C . Other vectors do change direction. In case, if the eigenvalue is negative, the direction of the transformation is negative. Now, if A is invertible, then A has no zero eigenvalues, and the following calculations are justified: so λ −1 is an eigenvalue of A −1 with corresponding eigenvector x. •However,adynamic systemproblemsuchas Ax =λx … • If λ = eigenvalue, then x = eigenvector (an eigenvector is always associated with an eigenvalue) Eg: If L(x) = 5x, 5 is the eigenvalue and x is the eigenvector. detQ(A,λ)has degree less than or equal to mnand degQ(A,λ)

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