Practice: Complex Eigenvalues and Eigenvectors Find the eigenvalues and eigenve…

Complex Eigenvalues

4 Activities

Practice: Complex Eigenvalues and Eigenvectors
Find the eigenvalues and eigenvectors of A=[−6−2012]A=\left[\begin{array}{rr}
-6&-20\\1&2
\end{array}\right]A=[−61​−202​].

A) λ1=−2−iλ2=−2−ix⃗1=[2−i1]x⃗2=[2+i1]\begin{array}{c|c}
\lambda_1=-2-i \quad & \quad 
\lambda_2=-2-i \\[0.5em]

\vec x_1 = \begin{bmatrix} 2-i\\1 \end{bmatrix}
& \quad
\vec x_2 = \begin{bmatrix} 2+i\\1 \end{bmatrix}
\end{array}λ1​=−2−ix1​=[2−i1​]​λ2​=−2−ix2​=[2+i1​]​

B) λ1=−1−2iλ2=−1+2ix⃗1=[2−i1]x⃗2=[2+i1]\begin{array}{c|c}
\lambda_1=-1-2i \quad & \quad 
\lambda_2=-1+2i \\[0.5em]

\vec x_1 = \begin{bmatrix} 2-i\\1 \end{bmatrix}
& \quad
\vec x_2 = \begin{bmatrix} 2+i\\1 \end{bmatrix}
\end{array}λ1​=−1−2ix1​=[2−i1​]​λ2​=−1+2ix2​=[2+i1​]​

C) λ1=−2+2iλ2=−2−2ix⃗1=[14+2i]x⃗2=[14−2i]\begin{array}{c|c}
\lambda_1=-2+2i \quad & \quad 
\lambda_2=-2-2i \\[0.5em]

\vec x_1 = \begin{bmatrix} 1\\4+2i \end{bmatrix}
& \quad
\vec x_2 = \begin{bmatrix} 1\\4-2i \end{bmatrix}
\end{array}λ1​=−2+2ix1​=[14+2i​]​λ2​=−2−2ix2​=[14−2i​]​

D) λ1=−2+2iλ2=−2−2ix⃗1=[−4+2i1]x⃗2=[−4−2i1]\begin{array}{c|c}
\lambda_1=-2+2i \quad & \quad 
\lambda_2=-2-2i \\[0.5em]

\vec x_1 = \begin{bmatrix} -4+2i\\1 \end{bmatrix}
& \quad
\vec x_2 = \begin{bmatrix} -4-2i\\1 \end{bmatrix}
\end{array}λ1​=−2+2ix1​=[−4+2i1​]​λ2​=−2−2ix2​=[−4−2i1​]​

I don't know

Practice: Complex Eigenvalues and Eigenvectors Find the eigenvalues and eigenve…

Related Topics

Complex Eigenvalues

Practice: Complex Eigenvalues and Eigenvectors