Question

Consider the given matrix. 3 0 0 0 2 0 4 0 1 find the eigenvalues. (enter your answers as a comma-separated list.)

Answer 1

`\begin{vmatrix}3-\lambda&0&0\\0&2-\lambda&0\\4&0&1-\lambda\end{vmatrix}=(3-\lambda)\begin{vmatrix}2-\lambda&0\\0&1-\lambda\end{vmatrix}=0`

`=(3-\lambda)(2-\lambda)(1-\lambda)`

`\implies\lambda_1=1,\lambda_2=2,\lambda=3`