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3. Find all eigenvalues and eigenvectors of the matrix -20 2 -1 0 2 0-2 1

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Solution: Given Matrix -2 o 2 1 let A= 2 -2 Characters tics polynomil will be given as |A-x1) = 0 2 2 -2-1 se (-2-7) (-x) (-2Eigen vector for Eigen value a, = -4 (-2-(-4) o 2 2 -(-4) =o 1 y 2 0 -2-E4) Z Eigen vector 2 0 2 1 4 2 2 Performing now operaNow for d₂ = 3=0 -2-0 0 2 - 0 2 - 2-0 - 2 0 2 - 0 2 -2 using now operation R3 Rz TRI 2 0 Noo ] RI R / -2 [. ::] [:) - x + z =

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3. Find all eigenvalues and eigenvectors of the matrix -20 2 -1 0 2 0-2 1
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