Thread: Eigenvalues for 3x3 Matrix

Trying to find eigenvalues for this matrix



If my math is correct, the determinant of this is , but this doesn't factor, so I don't know how to find the roots.

Can somebody help? Thanks.

your math is incorrect.

the determinant is:

(1 - λ)³ - (-2)(-2)(1 - λ) - (2)(2)(1 - λ) = 1 - 3λ + 3λ² - λ³ - 8(1 - λ) = -7 +5λ + 3λ² - λ³

this has one rational root, and two irrational roots which are "conjugate" (in the sense of square roots).