Question

point) Suppose that the trace of a 2 x 2 matrix A is tr(A)= -9 and the determinant is det(A) 18. Find the eigenvalues of A. The eigenvalues of A are (Enter your answers as a comma separated list.)

Answer 1

Answer with explanation:

Matrix A= (2 × 2) Matrix

Trace A= -9

Also,Determinant A= |A|=18

⇒Characteristics Polynomial is given by

Δ(A)=A² -A ×trace (A)+Determinant (A)

=A²+9 A+18

=(A+6)(A+3)

So, eigenvalues can be obtained by substituting :

 Δ(A)=0

(A+6)(A+3)=0

A= -6 ∧ A= -3

Two Eigenvalues are = -6, -3