A spherical conducting shell has charge -5 C. A particle with charge -8 C is placed at the center of the cavity. The charges (in C) on the inner surface and on the outer surface of the shell, respectively, are:

Explanation:

The charge of - 5C will be spread  on the outer surface of the shell . The presence of - 8C charge at the Centre will create + 8C charge on the inner surface and - 8C charge on the outer surface . The result is that the total charge on the outer surface of the shell will be - 5C + - 8C = - 13C and the inner surface will have charge of + 8C . + 8C charge will be locked to centrally situated - 8C charge and will not be neutralized by negative charge of outer surface .

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i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.