Let M {\displaystyle {}M} be an m × n {\displaystyle {}m\times n} - matrix. Show that the matrix product M e j {\displaystyle {}Me_{j}} of M {\displaystyle {}M} with the j {\displaystyle {}j} -th standard vector (regarded as a column vector) is the j {\displaystyle {}j} -th column of M {\displaystyle {}M} . What is e i M {\displaystyle {}e_{i}M} , where e i {\displaystyle {}e_{i}} is the i {\displaystyle {}i} -th standard vector (regarded as a row vector)?
