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(Solved): Find the eigenvalues and associated eigenvectors of the given matrix A A=222 ...


Find the eigenvalues and associated eigenvectors of the given matrix A \[ A=\left[\begin{array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -

2. Determine whether or not the given matrix \( \mathrm{A} \) is diagonalizable. If it is, find a diagonalizing matrix \( \ma

Find the eigenvalues and associated eigenvectors of the given matrix A 2. Determine whether or not the given matrix is diagonalizable. If it is, find a diagonalizing matrix and a diagonal matrix D such that


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Part 1:- To find the eigenvalues and eigenvectors of matrix A, we need to solve the characteristic equation and then solve for the eigenvectors corresponding to each eigenvalue.

First, we find the characteristic equation by computing the determinant of the matrix A - ?I, where I is the identity matrix and ? is an eigenvalue:



Expanding along the first row, we get:



This gives us the characteristic equation:

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