Question

Find all possible real values λ such that det(A − λI3) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) A = −5 −4 −9 0 0 2 0 0 8

Answer 1

Answer:

λ = 8,-5,0

Step-by-step explanation:

given matrix,

A = $\left[\begin{array}{ccc}-5&-4&-9\\0&0&2\\0&0&8\end{array}\right]$

det (A − λI) = 0

A − λI = 0

$\left[\begin{array}{ccc}-5&-4&-9\\0&0&2\\0&0&8\end{array}\right]$-λ $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$=0

$\left[\begin{array}{ccc}-5-\lambda&-4&-9\\0&-\lambda&2\\0&0&8-\lambda\end{array}\right]$=0

now finding determinant

( 8-λ){ (-5-λ)(-λ)- 0} = 0

λ = 8,-5,0