3. Consider the following matrix 3 0 A = -1 1 0 (a) Calculate all of...

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3. Consider the following matrix 3 0 A = -1 1 0 (a) Calculate all of the eigenvalues of A. (b) For each eigenvalue of A found in (a), find a basis for the corresponding eigenspace. (c) Determine whether the collection of all basis vectors found in (b) is linearly dependent or linearly independent. (d) Is the matrix A diagonalizable? Explain why or why not. 3. Consider the following matrix 3 0 A = -1 1 0 (a) Calculate all of the eigenvalues of A. (b) For each eigenvalue of A found in (a), find a basis for the corresponding eigenspace. (c) Determine whether the collection of all basis vectors found in (b) is linearly dependent or linearly independent. (d) Is the matrix A diagonalizable? Explain why or why not.