Assume X,Y,Z,W and P are matrices of order 2 x n, 3 x k, 2 x p, n x 3, and p x k respectively.
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
Assume X,Y,Z,W and P are matrices of order 2 x n, 3 x k, 2 x p, n x 3, and p x k respectively.
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
Solution and Explanation
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 n × 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 n × 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, k = 3 and p = n are the restrictions on n, k, and p so that will be defined.
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