The restriction o

Matrices P and Y are of the orders p × k and 3 × k respectively.

Therefore, matrix PY will be defined if k = 3.

Then, PY will be of the order p × k.

Matrices W and Y are of the orders n × 3 and 3 × k respectively.

As, the number of columns in W is equal to the number of rows in Y, Matrix WY is well defined and is of the order n × k.

Matrices PY and WY can be added only when their orders are the same.

Therefore, PY is of the order p × k and WY is of the order n × k.

Thus, we must have p = n.

Therefore, k = 3 and p = n are the restrictions on n, k and p so that

PY + WY will be defined.