Final answer:
The addition of two different matrices can be nonsymmetric.
Step-by-step explanation:
The answer to the question is c) No, but they are mutually exclusive. When adding two matrices, the resulting sum will always be symmetric as long as the matrices being added are symmetric themselves. This is because the sum of two symmetric matrices will preserve the symmetry property, resulting in a symmetric matrix. However, if the matrices being added are not symmetric, then the resulting sum can be nonsymmetric.
An example of this is:
Matrix A = [1 2; 3 4]
Matrix B = [5 6; 7 8]
The sum of A and B, denoted as A + B, is:
A + B = [1+5 2+6; 3+7 4+8] = [6 8; 10 12]
As you can see, the resulting sum matrix is nonsymmetric.