Question

Assume that Y,W,P are matrices of order 3×k ,n×3 and p×k respectively. Find the restrictions on n,p,k so that PY +WY is defined.

Answer 1

P and Y are of order p*k and 3*k respectivly.

\therefore PY will be defined only if k=3, i.e. order of PY is p*k.

W and Y are of order n*3 and 3*k respectivly.

\therefore WY is defined because the number of columns of W is equal to the number of rows of Y which is 3, i.e. the order of WY is n*k

Matrices PY and WY can only be added if they both have same order i.e = n*k implies p=n.

Thus, k = 3, p = nare restrictions on n, k and p so that PY + WY will be defined.

So hence K=3P=n..

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