Matrix A and vector b are defined by
(a) Solve the linear system of equations Ax = b using MATLAB.
(b) Find A-1 and verify that A-1 A = I, where I is the 6X6 identity matrix. Compute x = A-1b using MATLAB and check the result with that of (a).
(c) Compute the determinant of A.
(d) Take matrix A' as A' = A + AT, where AT is the transpose of A . Using MATLAB, solve the linear system of equations A'x = b.
(e) Take matrix S as
Compute the rank of S manually and use the MATLAB function to verify the result.