Given the matrix $A = egin{bmatrix} 1 & 2 \ 3 & 2 end{bmatrix}$ \ a) Determine which of the following vectors are eigenvectors of \ A \ $v_1 = egin{bmatrix} 0 \ 1 end{bmatrix}$, $v_2 = egin{bmatrix} 2 \ 3 end{bmatrix}$, $v_3 = egin{bmatrix} -1 \ 4 end{bmatrix}$, $v_4 = egin{bmatrix} 1 \ -1 end{bmatrix}$, \ $v_5 = egin{bmatrix} -3 \ 3 end{bmatrix}$ \ b) Find the corresponding eigenvalues for each eigenvector.
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To do this, we need to solve the characteristic equation, which is given by: $$\text{det}(A - \lambda I) = 0$$ Where $\lambda$ is the eigenvalue and $I$ is the identity matrix. For the given matrix A: $$A = \begin{bmatrix} 1 & 2 \\ 3 & 2 \end{bmatrix}$$ So, Show more…
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