Answer:
Step-by-step explanation:
We have to diagonalize the matrix
[tex]\left[\begin{array}{ccc}1&-1&0\\5&1&4\\0&1&1\end{array}\right][/tex]
we have to solve the expression
[tex]|A-\lambda I|=0[/tex]
Thus, by applying the determinant we obtain the polynomial
[tex](1-\lambda )^3+5-4=0\\(1-\lambda )^3+1=0\\[/tex]
[tex]-\lambda^3+3\lambda^2-4\lambda+2[/tex]
[tex]\lambda_1=1\\\lambda_2=1-i\\\lambda_3=1+i\\[/tex]
and the eigenvector will be
[tex]v_1=(-4,0,5)\\v_2=(-1,-i,-1)\\v_3=(-1,i,1)[/tex]
HOPE THIS HELPS!!
