Linear Algebra Quiz
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EIGENVALUES & EIGENVECTORS
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Let A=(2−14−1)A = \begin{pmatrix} 2 & -1 \\ 4 & -1 \end{pmatrix}. If v1\mathbf{v}_1 and v2\mathbf{v}_2 are eigenvectors corresponding to distinct eigenvalues λ1\lambda_1 and λ2\lambda_2 respectively, and v1+v2=(35)\mathbf{v}_1 + \mathbf{v}_2 = \begin{pmatrix} 3 \\ 5 \end{pmatrix}, what is A(v1+v2)A(\mathbf{v}_1 + \mathbf{v}_2)?
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