Question: Please help me solve this question. Thank you! 3. Let A be a 3 X 3 matrix whose eigenvalues are 1 )u = 1 A2

Please help me solve this question. Thank you!

3. Let A be a 3 X 3 matrix whose eigenvalues are 1 )u = 1 A2 = 1 A3 = E and whose corresponding eigenvectors are (a) What. is nullity (A I)? What is rank (A I)? Explain. (b) What is nullity,r (A)? What is rank (A)? Explain. 1 (c) If in. = [1] and E]; = Akin, does lim Ek exist and if so what is it? (Hint: kroo 1 53 = E1 + E3.)

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