Consider M be space of all 2 x 3 matrices.
i) Determine the basis for subspace S having of matrices in M whose columns add to zero.
ii) Determine the basis for subspace T having matrices in M whose rows add to zero.
iii) Determine the basis for subspace S \bigcap T of M. This is set of matrices whose rows and columns add to zero.
iv) Determine the basis of subspace U of M whose nullspace contains (2, 1, 1).