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I don't know where to start with.. so please give me detailed steps.

Question 4 (30 marks) Let F =(yz +zcosx)i +(cxz )j + (xy + sin x)k , where c is a constant. (a) Find the constant c such that F is irrotational. (10 marks) (b) With c obtained in (a), find a potential function @ such that Vo= F. (10 marks) (c) Evaluate [F . dr , where C is the path from point A(0, 0, 0) to point B point B(5, 1,1 ) . (10 marks)Question $ ( 30 marks ) Given a 3 X 3 real matrix '96 3 '0. 96 0.03 0. 014 I A = - 100 96 1 0. 03 0. 96 0. 01 . 1 1 98 / 10.01 0. 01 0. 98 det ( A ) = 0. 9021 , and det ( A - 21 ) = 1A - 211 = - ( 1 - 1) ( 1 - 0. 93 ) (2 - 0 ), where I is a 3 x 3 identity matrix , ( a ) find the eigenvalue c of matrix A , and find the eigenvectors corresponding to each of the three eigenvalues ; ( 14 marks ) ( b) find a diagonal matrix D and an invertible matrix P such that AP = PD ;] ( 4 marks ) ( C ) is PIP = I ? If not , find P -! ; ( 4 marks ) ( d ) from ( a ) - ( C ) , or otherwise , deduce the eigenvalues and eigenvectors of matrix C , where* C = AZ + A + !. Note : do not attempt to compute matrix C ] . ( 4 marks ) ( e ) assuming 71000 = 0 for O CA