# Assume X, Y, Z, W and P are matrices of order, and respectively. The restriction on n, k and p so that will be defined are:

Question:

Assume XYZW and P are matrices of order, and respectively. The restriction on nk and p so that 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

Solution:

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

Therefore, matrix PY will be defined if k = 3. Consequently, PY will be of the order p × k.

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

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

However, PY is of the order p × k and WY is of the order n × k. Therefore, we must have p = n.

Thus, = 3 and p = n are the restrictions on nk, and p so that will be defined.

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