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Let A be a 7 x 7 diagonalizable matrix with three distinct eigenvalues lambda_1, lambda_2, and lambd ...

Let A be a 7 x 7 diagonalizable matrix with three distinct eigenvalues lambda_1, lambda_2, and lambda_3. Suppose the dimensions of the eigenspaces E_1 and E_2 associated to lambda_1 and lambda_2 are 2 and 3 respectively. What must the dimension of E_3, the eigenspace associated to lambda_3, be? Explain.

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