Answer to Question #298744 in Linear Algebra for fernu

Question

find the sum and product of eigenvalues of the matrix

[1 2 3

-1 2 1

1 1 1 ]

Answer 1

Sum of eigen values = sum of the principal diagonal elements

Hence sum = ( 1+2+1) = 4

Product of eigen values = determinant

Which is obtained as below

1(2-1) -2( -1-1) +3(-1-2)

Which becomes

1-2(-2)+3(-3) = 1+4-9 = -4 which is the required product