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Question: please help me solve the two questionsthanks...

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Please help me solve the two questions,thanks!
Question 15. (15 marks Let AE R3 be an unknown matrix, and Lat V 3). Assume ker(A+21)-spantn and ker(A-J)-span(mv) (1). ( marks) Prove that A is diagonalizable. Then find the minimal polynomial of A (2). (10 marks) Compute the matrix A
Question 12. (15 marks). Suppose that W is a finite dim ensional vector spaces and T : V → W is a linear transformation. Prove that T is injective if and only if there exists a linear transformation S:W+V such that ST is the identity map on
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