Question

Consider the given matrix. 1 −1 0 5 1 4 0 1 1 Find the eigenvalues. (Enter your answers as a comma-separated list.) λ = Find the eigenvectors. (Enter your answers in order of the corresponding eigenvalues, from smallest to largest by real part, then by imaginary part.)

Answer 1

Answer:

Step-by-step explanation:

We have to diagonalize the matrix

$\left[\begin{array}{ccc}1&-1&0\\5&1&4\\0&1&1\end{array}\right]$

we have to solve the expression

$|A-\lambda I|=0$

Thus, by applying the determinant we obtain the polynomial

$(1-\lambda )^3+5-4=0\\(1-\lambda )^3+1=0$

$-\lambda^3+3\lambda^2-4\lambda+2$

$\lambda_1=1\\\lambda_2=1-i\\\lambda_3=1+i$

and the eigenvector will be

$v_1=(-4,0,5)\\v_2=(-1,-i,-1)\\v_3=(-1,i,1)$

HOPE THIS HELPS!!