Parts 41-44 Please **Problem III:**Let \( B \) denote the matrix given below.(i) Find all eigenvalues of the matrix \( B \).(ii) For each eigenvalue of \( B \), find an associated eigenvector.(iii) Is the matrix \( B \) diagonalizable? Explain.(iv) Find all eigenvalues of the matrix \( 2B + 3I \), where \( I \) is the identity matrix.Matrices:41.\[\begin{pmatrix}1 & 0 & 1 \\0 & 1 & 0 \\1 & 0 & 1 \end{pmatrix}\]42.\[\begin{pmatrix}1 & 0 & 1 \\0 & 3 & 0 \\1 & 0 & 1 \end{pmatrix}\]43.\[\begin{pmatrix}1 & 0 & 1 \\0 & -1 & 0 \\1 & 0 & 1 \end{pmatrix}\]44.\[\begin{pmatrix}1 & 0 & 1 \\0 & -2 & 0 \\1 & 0 & 1 \end{pmatrix}\]45.\[\begin{pmatrix}1 & 0 & 1 \\0 & -3 & 0 \\1 & 0 & 1 \end{pmatrix}\]46.\[\begin{pmatrix}1 & 0 & 1 \\0 & 2 & 0 \\1 & 0 & 1 \end{pmatrix}\]47.\[\begin{pmatrix}0 & 0 & 0 \\1 & 0 & 1 \\0 & 1 & 0 \end{pmatrix}\]48.\[\begin{pmatrix}0 & 0 & 0 \\2 & 0 & 1 \\0 & 1 & 0 \end{pmatrix}\]49.\[\begin{pmatrix}0 & 0 & 0 \\3 & 0 & 1 \\0 & 1 & 0 \end{pmatrix}\]50.\[\begin{pmatrix}0 &

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