Question

Find the sum of the eigen values A=[211 121 001]

Answer 1

Answer:

Theorem: If A is an n × n matrix, then the sum of the n eigenvalues of A is the trace of A and the product of the n eigenvalues is the determinant of A. Also let the n eigenvalues of A be λ1, ..., λn. Finally, denote the characteristic polynomial of A by p(λ) = |λI − A| = λn + cn−1λn−1 + ··· + c1λ + c0.

Step-by-step explanation:

Eigenvalues and Eigenvectors • If A is an n x n matrix and λ is a scalar for which Ax = λx has a nontrivial solution x ∈ ℜⁿ, then λ is an eigenvalue of A and x is a corresponding eigenvector of A. Ax=λx=λIx (A-λI)x=0 • The matrix (A-λI ) is called the characteristic matrix of a where I is the Unit matrix. • The equation det (A-λI )= 0 is called characteristic equationof A and the roots of this equation are called the eigenvalues of the matrix A. The set of all eigenvectors is called the eigenspace of A corresponding to λ. The set of all eigenvalues of a is called spectrum of A.

Answer 2

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