Question

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 1

(A) k = 3, p = n

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The order of matrix P is p x k
and the order of matrix Y is 3 x k.
PY is defined, when
No. of columns in P = No. of rows in Y.
⇒ k = 3
∴ The order of PY is p x 3.
Now, the order of W is n x 3.
The order of Y is 3 x k.
WY is defined, when
No. of columns in W = No. of rows in Y = 3.
So, WY is defined.
The order of WY = n x 3. .
Matrix PY + WY is defined when PY and WY are of the same order.
But they are of the order p x 3 and nx 3 respectively.
⇒ PY + WY is defined when p = n.
Hence, PY + WY is defined when k = 3 and p = n.