Question

find the sum and product of the eigen values of the matrix A=​

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.