Results of rank and determinant for symbolic matrix do not consist with each other.

Hi, guys,

I am currently dealing with some symbolic derivation. Some 6 by 6 matrix A contains variable theta2 and theta3 is constructed. Also, the following constraint was set.

    theta2 = -acos(cos(theta3)/(-cos(theta3)-1));

However, when I use rank(A), it gives out 6, meanwhile simple(det(A)) gives 0. Obviously, one of them is wrong. I double checked the rank by using Maple, it should be 5. Also, the reality needs A to be of rank 5. Also, rref(A) gives out an 6 by 6 identity matrix.

I know this constraint requires -120<theta3<120. And I have tried using the following to give assumption for this variable:

    assume(theta3>-120 & theta3<120);

Am I doing this right?

Does anybody have similar issue with symbolic calculation in Matlab? The Mupad core is trustable or not?

My guess is rank(A) is not following the exact symbolic way. Do I need to call Mupad command to get rank? Will it make a difference?

Thanks for you guys' concern. Hope somebody discuss with me.