Question

Assume X,Y,Z, W and P are matrices of orders $2\times n,3\times k,2\times p,n\times 3andp\times k$ respectivley.

The restrictions on n,k and p so that PY+WY will be defined are
(a)k=3, p=n
(b)k is arbirary, p=2
(c)p is arbitary
(d)k =2, p =3

Answer 1

Matrices P and Y are of the orders $p\times k$ and $3\times k$ respectively.
Therefore, matrix PY wil be defined if k =3. Consequently, PY will be of the order p \times k. Matrices W and Y are of the orders $n\times 3and3\times k$ respectively.
Since, 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 $n\times k.$
Matrices PY and WY can be added only where their orders are the same.
However, PY is of the order $p\times k$ and WY is of the orders $n\times k$, therefore, we must have p =n. Thus, k=3 and p =n are the restrictions on n,k and p so that PY+WY will be defined. So, correct option is (a).