## anonymous one year ago For which value of k does the matrix A=[4 k; 2 −2] have one real eigenvalue of algebraic multiplicity 2? let lambda = x x^2 -2x + (-8-2k) = 0

1. perl

The eigenvalues of A are x, where det(A-x*Identity) = 0. $$\Large{\det \begin{bmatrix} 4-x & k \\2& -2-x \end{bmatrix}=0 \\ ~\\\iff \\~\\ x^2-2x-2k-8=0 }$$

2. perl

3. anonymous

thank you perl :)

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