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Linear AlgebraEasyDiagonalization & Matrix Powers

Diagonalization & Matrix Powers · Easy problem

Let A=(4123)A = \begin{pmatrix}4 & 1\\2 & 3\end{pmatrix}. The vector v=(11)\mathbf{v} = \begin{pmatrix}1\\1\end{pmatrix} is an eigenvector of AA. Find the first entry of A3vA^3\mathbf{v}.