(e) For a given symmetric matrix A e RMXM, and A e R, the set S = XE RM Ax = Ax (f) The set of matrices: S = XE RMXM EXii = 03. Problem 3: Which of the following sets form a subspace? If yes, prove they are a subspace and find its basis, and dimension. T (a) S1 = x = x1 X2 X3 E IR3 X1+ X2 + X3 = 01 T (b) S2 = x = x1 X2 x3 ER3 x1+ x2 + 13 = 1 T (c) $3 = x = X1 X2 X3 X4 E R4 X1X4 = X2X3 T (d) S3 = x= x1 X2 X3 X4 12 x3 X4 ERY 1 1 = - 12 12 + 13 + 14 = 06