Q. 213.8( 33 Votes )

The restriction on n, k and p so that PY + WY will be defined are:
A. k = 3, p = n

B. k is arbitrary, p = 2

C. p is arbitrary, k = 3

D. k = 2, p = 3

Answer :

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.

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