What are the eigenvalues of the following 2 x 2 matrix?

( 2 -1 )
(-4 5 )

A. -1 and 1
B. 1 and 6
C. 2 and 5
D. 4 a...

Question

What are the eigenvalues of the following 2 x 2 matrix?

( 2   -1 )
(-4    5 )

A. -1 and 1
B. 1 and 6
C. 2 and 5
D. 4 and -1

Accepted Answer

Eigenvalues are 1 and 6 For a 2x2 matrix, the characteristic equation is lambda^2 - (trace)*lambda + (det) = 0. The trace is the sum of diagonal elements and the determinant is ad - bc. Solving this quadratic gives the two eigenvalues. This is much faster than full cofactor expansion.

What are the eigenvalues of the following 2 x 2 matrix? ( 2 -1 ) (-4 5 ) A. -1 and 1 B. 1 and 6 C. 2 and 5 D. 4 and -1